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• The dynamic behavior of droplets floating through the holes is studied. • The recommended range of dimensionless parameter Bo m is given. • Magnetic fields can effectively control the generation of secondary droplets. In this study, we utilize the simplified lattice Boltzmann method (SLBM) to investigate numerically the motion of buoyancy-driven deformable ferrofluid droplets through the orifice of varying widths and depths in two-dimensional (2D) space. Positioned directly beneath a plate with a central hole, the magnetic fluid droplets undergo acceleration to meet the plate under the influence of buoyancy and magnetic forces. We investigate the impact of magnetic field strength (Bo m), pore ratio (PR), plate thickness ratio (WR), droplet viscosity (Re), and the plate's wettability (contact angle) on the dynamic behavior of ferrofluid droplets ascending through the orifice. Our results reveal significant effects on the efficiency and morphology of ferrofluid droplets passing through the hole. The introduction of a magnetic field facilitates a larger volume of liquid droplets passing through the hole at PR = 0.25. Moreover, increasing magnetic field intensity leads to the generation of secondary droplets during passage through the orifice. In practical applications, to prevent the generation of secondary droplets, we recommend Bo m < 3 when the pore ratio falls within 0.35 < PR < 0.45 and plate thickness ratio WR = 1. Additionally, with increasing obstacle thickness, ferrofluid droplets on the hydrophobic wall can pass through the orifice more easily. Furthermore, when the magnetic field strength exceeds a certain threshold (Bo m = 6.08), the droplets can pass through the orifice regardless of the wall's hydrophilicity or hydrophobicity. For practical applications with the pore ratio PR = 0.25 and plate thickness ratio WR > 1, we suggest Bo m > 3. [ABSTRACT FROM AUTHOR]

In clouds and under cold weather, water droplets impact and freeze on aircraft structures. The Eulerian model for the droplet flow predicts the impinging water mass. The model equations are close to the Euler equations but without the pressure term, known as pressureless Euler model. Consequently, the resulting system is only weakly hyperbolic and standard Riemann solvers strongly relying on the eigenstructure of the system cannot solve the Eulerian model. To circumvent this problem, the model is supplemented with an extra-term mimicking the divergence of a particle pressure. The main purpose of this work is to implement a multidimensional aware Riemann solver for a Finite Volume simulation code for the modified formulation of the Eulerian droplet model. The numerical method should preserve physical properties such as the positivity of the liquid water content, and must produce accurate results without sacrificing the general robustness. The flow around a cylinder assess the numerical method in 2D on radial meshes. • New multidimensional Riemann solver for the modified formulation of the Eulerian droplet model. • This model is only weakly hyperbolic. An additional term is added. • The multidimensional Riemann solver is derived and adapted to the Eulerian droplet model. • The proposed method, preserves physical properties such as positivity, is accurate and robust. [ABSTRACT FROM AUTHOR]

• A 3D pseudo-potential multiphase model is developed. • The model is capable of achieving gas-liquid super-large density ratio. • The model is able to adjust surface tension independently of density ratio. • The numerical stability keeps well in the simulations with large density ratio and high Reynolds number. In this paper, an improved three-dimensional pseudo-potential multiphase flow model is proposed. A high-precision difference scheme is employed to improve the computational accuracy of the interaction forces to achieve super-large density ratio. The present model is verified to obtain two-phase density ratio up to hundreds of thousands for all selected equations of state, and the spurious currents can be suppressed to a relatively low level. A modification pressure tensor is introduced to implement a wide range of surface tension adjustments independently of the density ratio. The model is applied to simulate droplet impacts on a liquid film as well as droplet impacts on a dry surface. Numerical results show that the model still has good numerical stability in simulating complex fluid problems with very large density ratio, adjustable surface tension, high Reynolds number, or containing the wettable surface. In addition, to improve the computational efficiency, an efficient parallel algorithm based on graphics processing unit (GPU) is designed for the present model. A maximum speedup ratio of 687 times is obtained compared to the corresponding CPU-based serial algorithm, which can significantly accelerate the numerical simulation study. [ABSTRACT FROM AUTHOR]

The Richtmyer–Meshkov (RM) instability widely exists in variety of industrial and scientific applications, such as in inertial confinement fusion, astrophysics explosions, supersonic combustion, bubble dynamics and cavitation. This study investigates the unfolding physical phenomena of RM instability at SF 6 elliptical bubbles using numerical simulations. In contrast to cylindrical bubble, both shocked horizontal/vertical-aligned elliptical bubbles with different aspect ratios are considered, emphasizing the aspect ratio effects on flow morphology, complex wave patterns, interface deformation, vorticity generation, and interface features. For this purpose, a two-dimensional system of compressible Navier–Stokes–Fourier equations for multicomponent flows are solved using by a mixed modal discontinuous Galerkin method. Numerical simulations illustrate that the aspect ratio of elliptical bubbles have a significant influence on the vortex dynamics and the associated RM instability flows in contrast to the cylindrical bubble. In horizontal-aligned elliptical bubbles, some additional complex waves pattern, including inward jet and secondary vortex rings are observed. While, in vertical-aligned elliptical bubbles, the interface between two primary vortex rings is always vertical and has a "hippocampus" appearance due to the enhancement of downstream velocity. The baroclinic vorticity due to misalignment of density and pressure gradients at interface affects the bubble deformation and induces the Kelvin–Helmholtz instability, which leads to turbulent mixing. It is observed that the complexity of the vorticity fields is enhanced with increasing aspect ratios. Further, these aspect ratio effects result in integral diagnostic of important spatially integrated fields, and various interface features. • Simulations for shocked hydrodynamic instability at elliptical bubbles are performed. • Mixed modal DG solver is developed for compressible viscous multicomponent flows. • Thorough analysis of vortex dynamics between elliptical and cylindrical bubbles is conducted. • Detailed discussion on integral diagnostic and interface features are presented. [ABSTRACT FROM AUTHOR]

In thermal multiphase flows, the modulation in the heat transfer rate due to the presence of finite-size solid particles attract growing interest in recent years. This study focuses on developing a robust and efficient simulation method for particle-laden Rayleigh-Bénard convection. The present work utilizes the double distribution function-based thermal lattice-Boltzmann method (TLBM), which enables successful simulations of multiphase fluid-thermal interactions. The no-slip boundary of the moving solid particles is handled by the interpolated bounce-back scheme. Additionally, Galilean invariant momentum exchange and heat exchange approaches are employed for hydrodynamic force and heat transfer calculation at the solid boundaries. The accuracy of the current method is verified with several benchmark cases, including three-dimensional single-phase Rayleigh-Bénard convection, as well as the settling of hot and cold spherical particles in a three-dimensional enclosure. Furthermore, we explore the modulation of Rayleigh-Bénard flows due to the presence of freely moving finite-size particles. The simulations are conducted on a distributed memory cluster with a 3D domain decomposition technique facilitated by the MPI library. A brief discussion on the parallel performance of the simulations is provided for both particle-laden and single-phase flow scenarios. Finally, the effects of finite-size solid particles on the overall heat transfer efficiency and modulation to the flow field in three-dimensional particle-laden turbulent Rayleigh-Bénard convection are discussed. The results show that addition of solid particles results in a moderate increase in the overall Nusselt number, and this enhancement is mainly due to the increased heat flux transported by the particles. • A mesoscopic method for 3D particle-laden thermal flows was developed and validated. • Modulation of 3D particle-laden Rayleigh-Bénard convection flows was studied. • Addition of particles results in a moderate increase in the overall Nusselt number. • This increase is caused by the increased heat flux carried by the moving particles. • The particles damp large-scale fluctuations, but enhance small-scale fluctuations. • The distribution functions are explicitly related to the hydrodynamic fields. [ABSTRACT FROM AUTHOR]

On the basis of previous work, we propose a phenomenological computable Boltzmann model equation synchronously involving polyatomic molecular internal energies, dissociation and recombination effects for multicomponent gases in this paper. Here, the distribution functions of each species have nine independent variables, which are time, physical space, molecular velocity, rotational energy and vibrational energy, if this component is a polyatomic gas. In this model equation, the concept of 'chemical reaction rate' is introduced in the chemical collision term to characterize the affect of chemical reactions. In order to make this complex model equation being 'computable', reduced distribution functions are adopted to get rid of two independent variables about rotational energy and vibrational energy of polyatomic component. We prove the conservation of this model equation, and then numerically solve it by the framework of gas-kinetic unified algorithm (GKUA), which is one kind of discrete velocity method (DVM). Here, non-catalytic boundary condition is adopted. Finally, a simple hypersonic flow around a cylinder with Mach number being 24.85 is numerically simulated to verify this model equation. In this case, four different components and eight chemical reactions are considered. It is shown that, this proposed Boltzmann model equation has the potential to be used to simulate thermochemical non-equilibrium effects of hypersonic flows covering various regimes. • A computable kinetic model involving polyatomic molecular internal energies and chemical reaction effects, including dissociation and recombination, is presented for hypersonic flows of multicomponent mixed gases. • The conservation laws of mass, momentum and energy of this model are analyzed for each component and entire system. • The gas-kinetic unified algorithm (GKUA) is developed to numerically solve the proposed kinetic model and is preliminarily verified by comparing its results with those of the DSMC method for a hypersonic flow case. [ABSTRACT FROM AUTHOR]

In this paper, a multiple-relaxation-time lattice Boltzmann (LB) approach is developed for the simulation of three-dimensional (3D) liquid–vapor phase change based on the pseudopotential model. In contrast to some existing 3D thermal LB models for liquid–vapor phase change, the present approach has two advantages: for one thing, some gradient terms, such as the gradient of volumetric heat capacity and the Laplacian term of temperature, that must be computed with finite-difference scheme in previous works is not needed for the present thermal model. For another, the current model is constructed based on the seven discrete velocities in three dimensions (D3Q7), making it more efficient and much easier to be implemented. Also, based on the scheme proposed by Zhou and He (1997), a pressure boundary condition for the D3Q19 lattice is proposed to model the multiphase flow in open systems. This model is then validated by considering the temperature distribution in a 3D saturated liquid–vapor system, the d 2 law, the droplet evaporation on a heated surface and the nucleate boiling. It is observed that the numerical results fit well with the analytical solutions, and the results of the finite difference method or the experimental data. Our numerical results indicate that the present approach is reliable and efficient in dealing with the 3D liquid–vapor phase change. • An efficient LB model to simulate 3D liquid–vapor phase change is proposed. • The current model is constructed based on the D3Q7 lattice. • This method needs not calculate the density gradient. [ABSTRACT FROM AUTHOR]

Artificial upwelling by the use of airlift pump is regarded as an effective way in utilizing deep ocean water and actualizing ocean fertilization. This paper focuses on numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system based on one-dimensional multi-fluid model. The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are calculated by solving the governing equations or by integrating the vector form of nonhomogeneous ordinary differential equation for two-phase flow interval. Upon successful verification of the present numerical model through a comparison with precedent theoretical and experimental results in case of a vertical pipe with length of 7.86 m, the model is extended to the case of artificial upwelling from water depth of 2000 m. The effects of submerged depth of air–water mixer on the pumped amount of water and the depth distributions of 6 physical quantities are considered. • This paper is concerned with numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system to lift deep ocean water. • The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are obtained from one-dimensional multi-fluid model. • The present model can be applied to predict the performance of airlift pump for lifting deep ocean water and the depth distributions of 6 physical quantities in axial direction. [ABSTRACT FROM AUTHOR]

Liquid–vapor phase change in the presence of non-condensable gases is a classical problem, which continues to challenge continuum modeling. Here, we propose a new model based on the phase field method, which describes the dynamics of the non-condensable gas, phase change and flow simultaneously. The model is built by extending van der Waals and Korteweg's theory for phase-transforming mixtures. The model equations have fourth order partial differential operators which presents significant challenges to standard spatial discretization methods. In addition, the isentropic form of the model equations is not hyperbolic at the liquid–gas interface, which inhibits the direct application of most algorithms for systems of hyperbolic equations. We propose a novel numerical scheme based on Isogeometric Analysis and the Taylor–Galerkin method, and also implement a residual based discontinuity capturing scheme. We show numerical results, at micron length scales, to study the accuracy and stability of our algorithm. We study the flow of a shock wave past a liquid droplet to test our numerical algorithm when steep gradients are present in the solution. Finally, we use the model to study the problem of gas–vapor bubble collapse near a solid wall. • We propose a residual-based numerical scheme using Taylor–Galerkin discretization. • We show simulations of bubble collapse near a wall and shock wave past a droplet. [ABSTRACT FROM AUTHOR]

This work presents a Lagrangian meshless method for modeling transient heat transfer and thermo-capillary effects at the interface of two-phase incompressible fluids. To simulate the thermo-capillary effect, we add the Marangoni force to the continuum surface force (CSF) model, by considering the forces caused by the surface tension gradient which acts tangentially to the interface position. In the current study, we extend our previously proposed model which uses a fully explicit incompressible smoothed particle hydrodynamics (EISPH) approach along with corrected SPH and VKF kernel function, to obtain stable and accurate results in non-isothermal single and multi-phase problems. The model is validated for several test cases, including transient heat conduction, natural convection heat transfer, and thermo-capillary droplet migration, against conventional numerical methods. The validated model is used to study the effects of several dimensionless parameters on thermo-capillary droplet migration. The results show that the proposed EISPH method can model accurately complex heat transfer problems such as thermo-capillary induced motion. • We extend our fully explicit ISPH (EISPH) model to simulate non-isothermal problems. • Transient heat transfer and thermo-capillary droplet migration are investigated. • Proposed EISPH accurately models single and multi-phase transient heat transfer problems. [ABSTRACT FROM AUTHOR]

A new model for compressible multiphase flows involving sharp interfaces and phase change is presented, that uses a variant of the Volume-of-Fluid model to track phases by advecting their respective mass, and is hence called Mass-of-Fluid model. The framework is aimed at predicting the coupled multi-physical phenomena involved in most processes encountered in laser material processing, with the aim of minimizing a priori assumptions on the nature of the process. Emphasis is put on the multiphase fluid flow model, especially on the treatment of compressibility and phase change. The model's accuracy and suitability is demonstrated on problems of increasing complexity, including well-known benchmarks and problems encountered in laser material processing, where simulation results are compared to experimental observations. • Mass- and energy conservative, compressible multiphase model including phase changes. • Multiple segregated phases undergoing phase change and shocks are simulated. • No evaporation efficiency or recoil pressure term is needed. • Keyhole dynamics in additive manufacturing and welding are simulated. • Results are in good agreement with in-situ x-ray observations from literature. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for the sequential positioning, also called nested dissection, of two planes in an arbitrary polyhedron. Two planar interfaces are positioned such that the first plane truncates a given volume from this arbitrary polyhedron and the next plane truncates a second given volume from the residual polyhedron. This is a relevant task in the numerical simulation of three-phase flows when resorting to the geometric Volume-of-Fluid (VoF) method (Hirt and Nichols, 1981) with a Piecewise Linear Interface Calculation (PLIC) (Youngs, 1982). An efficient algorithm for this task significantly speeds up the three-phase PLIC algorithm. The present study describes a method based on a recursive application of the Gaussian divergence theorem, where the fact that the truncated polyhedron shares multiple faces with the original polyhedron can be exploited to reduce the computational effort. A careful choice of the coordinate system origin for the volume computation allows for successive positioning of two planes without reestablishing polyhedron connectivity. Combined with a highly efficient root finding, this results in a significant performance gain in the reconstruction of the three-phase interface configurations. The performance of the new method is assessed in a series of carefully designed numerical experiments. Compared to a conventional decomposition-based approach, the number of iterations and, thus, of the required truncations was reduced by up to an order of magnitude. The PLIC positioning run-time was reduced by about 90% in our reference implementation. Integrated into the multi-phase flow solver Free Surface 3D (FS3D), an overall performance gain of about 20% was achieved. The reference implementation of the efficient sequential PLIC positioning is available as a Fortran module at https://doi.org/10.18419/darus-2488. Allowing for simple integration into existing numerical schemes, the proposed algorithm is self-contained, requiring no external decomposition libraries. • Efficient sequential positioning of PLIC planes for multi-material cells. • Enhancement of the geometric VoF method for three-phase flows. • Numerical assessment with an extensive sample set of input data. • Performance insensitive with respect to volume fractions and normal orientations. • Significant performance gain both stand-alone and within a VoF flow solver. [ABSTRACT FROM AUTHOR]

• A high-order finite difference scheme for compressible multiphase flow is presented. • The scheme is based on weighted essentially non-oscillatory reconstruction. • The scheme applies the reconstruction on primitive field variables. • The scheme overcomes the difficulty of common schemes applied to multiphase flows. • The scheme is simple and more efficient than finite volume schemes. This paper presents a high-order weighted essentially non-oscillatory (WENO) finite difference scheme for compressible multi-fluid and multi-phase dynamics. The scheme overcomes the difficulty of applying the common flux-based WENO finite difference scheme to multi-fluid problems by applying the reconstruction on primitive variables and, thus avoiding the spurious oscillations inherent in the standard methods. Schemes of orders up to nine are introduced and analyzed. The proposed finite difference schemes are significantly more efficient than the available high-order finite volume schemes in both storage requirement, operation counts, and inter-processor message passing in parallel computations with efficiency gains being higher at higher orders and higher spatial dimensions. For the same level of accuracy, in three-dimensional calculations, a fourfold speedup or higher at fifth-order accuracy or higher over the finite volume scheme is expected. A comparison of the proposed scheme with the standard flux-based finite difference scheme in solving a single-fluid shock small entropy wave interaction is presented, demonstrating its excellent performance. In a challenging, two-fluid problem of a strong shock interacting with a helium-air interface, the accuracy, non-oscillatory, conservation, and convergence of the scheme are illustrated. Moreover, in a liquid water-air shock tube problem, the scheme effectively captures compression and expansion waves and contact discontinuity, and outperforms low-order schemes. In computations of a two-dimensional shock bubble interaction, good agreements with experimental data are obtained and competitive performance to the high-order finite volume scheme is shown. [ABSTRACT FROM AUTHOR]

• An adaptive variational multi-scale method for multiphase flows with surface tension is used to investigate the buckling of filaments of power-law fluids compressed at a constant velocity by two parallel pistons. • We analyse through almost 500 3D direct numerical simulations and scaling laws the capillary, viscous, and geometrical effects on the buckling of power-law fluid filaments under compression stresses. • The study is limited to cases in which the effects of both gravity and inertia are negligible. • We present regime diagrams showing where buckling occurs in the three-dimensional parameter space of capillary number, filament aspect ratio and rheological power-law exponent. Thanks to an adaptive variational multi-scale method for multiphase flows with surface tension, we investigate through direct numerical simulations and scaling laws the buckling of filaments of power-law fluids compressed at a constant velocity by two parallel pistons. Under low gravity (the Laplace pressure exceeds the hydrostatic pressure) and inertial conditions (very small Reynolds numbers), two regimes are observed for slender filaments: a first one driven by the capillary force and during which there is no deflection; and a second folding regime that is dominated by the compressive viscous force. The transition between these two scenarios is given by a critical capillary number, which in turn appears as an increasing function of the flow behaviour index. Our main results are summarised in two-dimensional phase diagrams whose axes are a slenderness parameter and the capillary number. [ABSTRACT FROM AUTHOR]

• We develop algebraic VOF schemes for material interface advection. • Newly designed TVD limiter yields crisp interface resolution. • Minimal amount of floatsam and jetsam. • Optimal accuracy is recovered within TVD-VOF schemes. • Computational efficiency comparable to geometric VOF. We revisit simple algebraic VOF methods for advection of material interfaces based of the well established TVD paradigm. We show that greatly improved representation of contact discontinuities is obtained through use of a novel CFL-dependent limiter whereby the classical TVD bounds are exceeded. Perfectly crisp numerical interfaces are obtained with very limited numerical atomization (flotsam and jetsam) as compared to previous SLIC schemes. Comparison of the algorithm with accurate geometrical VOF shows larger error at given mesh resolution, but comparable efficiency when the reduced computational cost is accounted for. [ABSTRACT FROM AUTHOR]

• A comprehensive multiphase SPH model is proposed. • A modified viscous term is incorporated into an improved boundary model. • Multiphase cases are tested to demonstrate the correctness of the model. Smoothed particle hydrodynamics is a typical Lagrangian meshless method, which has unique advantages in modelling multiphase phenomena with interface deformation and fragmentation. Current study proposes a comprehensive multiphase SPH model, which takes the advantages of some numerical techniques such as numerical interfacial force and damping technique. An improved boundary model is also introduced to deal with the solid walls. Additionally, the multiphase phenomena are investigated by solving an enhanced continuous surface force (CSF) model. In order to verify the proposed model, the droplet in shear flow is firstly considered and the results are consistent with the analytical solutions. Furthermore, the oscillations of square droplets are simulated under different particle resolutions, density and viscosity ratios. Finally, two and three dimensional bubble rising at high density ratios (up to 1000) are tested. [ABSTRACT FROM AUTHOR]

• A 3D non-orthogonal MRT lattice Boltzmann model is developed for multiphase flows. • The Chapman-Enskog analysis justifies that the model recovers the Navier-Stokes equations. • The numerical accuracy of orthogonal MRT model is retained with simpler implementation. In the classical multiple-relaxation-time (MRT) lattice Boltzmann (LB) method, the transformation matrix is formed by constructing a set of orthogonal basis vectors. In this paper, a theoretical and numerical study is performed to investigate the capability and efficiency of a non-orthogonal MRT-LB model for simulating multiphase flows. First, a three-dimensional non-orthogonal MRT-LB is proposed. A non-orthogonal MRT collision operator is devised based on a set of non-orthogonal basis vectors, through which the transformation matrix and its inverse matrix are considerably simplified as compared with those of an orthogonal MRT collision operator. Furthermore, through the Chapman-Enskog analysis, it is theoretically demonstrated that the three-dimensional non-orthogonal MRT-LB model can correctly recover the macroscopic equations at the Navier-Stokes level in the low Mach number limit. Numerical comparisons between the non-orthogonal MRT-LB model and the usual orthogonal MRT-LB model are made by simulating multiphase flows on the basis of the pseudopotential multiphase LB approach. The numerical results show that, in comparison with the usual orthogonal MRT-LB model, the non-orthogonal MRT-LB model can retain the numerical accuracy while simplifying the implementation. [ABSTRACT FROM AUTHOR]

• LBM based Gunstensen's color model is modified to include buoyancy effect. • The model can simulate deformation and drainage of bubble during coalescence. • The proposed model is verified against the benchmark problems in bubble coalescence. • The proposed model can simulate bubble flow for range of Re , Eo and Mo. The original Lattice Boltzmann method (LBM) based binary color model is modified to simulate three-dimensional buoyant multiphase flow. An effective force term is included during collision step in D3Q19 LBM to account for buoyancy force due to density contrast between fluid components. Buoyancy is not directly simulated as an effect of pressure gradients in the flow but was introduced from an analytical understanding of buoyancy effects due to density difference between the two phases. We are presenting results from three-dimensional numerical simulations to demonstrate the ability of the proposed approach to accurately predict the behavior of a single and multiple bubbles in a buoyant multiphase flow system. The effect of parameters such as grid size, viscosity ratio, surface tension, and interfacial thickness on the model accuracy are presented in this article. The shape and terminal velocity of bubbles in various flow regimes, characterized by the non-dimensional numbers (Eo, Mo, Re), are compared against experimental data and analytical model. The 3-D simulation results of Co-axial and oblique coalescence of a pair of bubbles from LBM simulations were found to be in good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

Highlights • Implicitly coupled solution of a multiphase flow model was developed. • Momentum interpolation based on temporal, drag, body force and pressure corrections. • Implicitly coupled solver was compared with its segregated counterpart. • Results were obtained for the backward-facing step and horizontal channel flows. • The implicitly coupled solver is more robust in cases with large drag coefficient. Abstract An implicitly coupled pressure–velocity transient scheme for the solution of the Eulerian multi-fluid model with any number of phases (MIC) was developed and implemented in OpenFOAM®. The numerical methodology is based on the phase-intensive momentum equations for the phase velocities and a pressure equation using a deferred-correction approach of the Rhie–Chow interpolation. An extension of the compact momentum interpolation method (CMI) to a system with any number of phases was developed. The developed methodology was tested against a segregated multiphase solver (MS) and a steady-state single phase solver, in cases considering up to four phases. The proposed method has proven to be more robust and accurate than the segregated counterpart, being able to converge in cases with large drag coefficients, providing time-step independent steady-state solutions. [ABSTRACT FROM AUTHOR]

Highlight • First report on the implementation of a new SGS model called AMD in OpenFOAM. • A thorough study on OpenFOAM-implemented AMD performance in benchmark and complex test cases. • High accuracy of AMD solutions compared to other SGS models despite using coarse grids. Abstract Minimum-dissipation sub-grid models represent simple alternatives to the Smagorinsky-type approaches to the implementation of sub-grid scales' (SGS) effects in the large-eddy simulation (LES) approach. Recently, the anisotropic minimum-dissipation (AMD) model has been introduced, which is a static type of eddy-viscosity SGS model and is a new addition to this family. This model is easy to implement; furthermore, not only can it consider the effect of various directions in computing sub-grid stress, it can also operate transitional flows from laminar to turbulent. For the first time, we implemented AMD in the open source package OpenFOAM. Foremost, we verified the OpenFOAM implementation of the AMD model for the prediction of isotropic decaying turbulence, a temporal mixing layer and an internal channel flow. To achieve this, decaying turbulence was considered for the isotropic turbulence produced by a grid with a mesh size of 5.08 × 10–2 m in a flow of mean velocity of 10 m/s. The temporal mixing layer was simulated at a Reynolds number based on half the initial vorticity thickness of 105. Channel flow was investigated at the three frictional Reynolds numbers of 180, 395 and 590. The verification results revealed that the implemented AMD model in OpenFOAM offered satisfactory accuracy to capture decaying turbulence and temporal mixing layer and calculate boundary layer velocity profiles and first and second-order turbulent parameters in the channel flow on anisotropic grids. Following this, for the first time, we evaluated AMD's performance in predicting external non-cavitating and cavitating flows over a 3D sphere. Non-cavitating and cavitating flow over the sphere were considered at Re = 2 × 104 and Re = 1.5 × 106, respectively. The AMD results were then compared with the direct numerical simulation (DNS) data and the numerical results obtained from the established SGS models such as dynamic Smagorinsky (DS), one equation eddy viscosity model (OEEVM), detached eddy simulation (DES), and delayed detached eddy simulation (DDES), where applicable. In treating sphere flow, in spite of the use of a coarse grid rather than the alternative SGS models, the AMD model predicted accurate results for pressure coefficient, shear stress, and separation point location over the sphere as well as the velocity profile in the wake region. It was detected that the simulation time of the AMD model was lower than that of DS in all the considered test cases by approximately 10–16%. [ABSTRACT FROM AUTHOR]

• Analyzed the LB thermal models with Chapman–Enskog expansion. • This analysis is verified in the simulation of single and two-phase heat transfer. • Compared the energy equations applied in the pseudo-potential modeling. Pseudo-potential lattice Boltzmann (LB) Methods have been widely applied in the gas-liquid multiphase flow and heat transfer simulations such as the bubble growth in the boiling process. Various formats of energy equations and discrete models are deduced to solve the heat transition in the simulations. However, the accuracy of these models has rarely been discussed. In this paper, four common LB thermal models are analyzed and numerically compared with the finite difference method by simulating the phenomena of single-phase natural convection and the one-dimensional heat transfer across the vapor-liquid interface. Simulation results show that all these LB thermal models lead to unwanted errors compared with the benchmark simulation results, while, with the proper discrete scheme, the finite difference method provides results with much better accuracy. With the presented finite difference model, we further compared the energy conservation of the energy equations in the phase change simulation. It is found that the accuracy and the thermodynamic consistency of the temperature-based energy equation is better than the internal-energy-based energy equation. [ABSTRACT FROM AUTHOR]

• Momentum and heat transfer of spheroids in supercritical water were studied. • Effects of incident angle, particle shape and Reynolds number were discussed. • Correlations for Cd and Nu of spheroids in SCW were established. This paper studies the effect of the incident angle (θ) on momentum and heat transfer of spheroids in supercritical water (SCW) based on numerical simulations. Both prolate and oblate spheroids are considered with the aspect ratio (Ar) ranging from 0.5 to 2.5. Numerical results show that both the drag coefficient (Cd) and average Nusselt number (Nu) of the oblate spheroid (Ar < 1) in SCW decrease with the increase of θ. Opposite trend is found for the prolate spheroid (Ar > 1). When θ ≤ 45° , both Cd and Nu of the two kinds of spheroids decrease with the increase of Ar. When θ > 45° , both Cd and Nu of the prolate spheroid increases with Ar. Nu of the oblate spheroid also increases with Ar but its Cd is dependent on the competition of friction and pressure. The effect of θ on Nu can be enhanced by either lifting Re or ∣ Ar-1 ∣. At last, the effect of θ is directly considered in the correlations of Cd and Nu for spheroids in SCW which can improve the accuracy of the multi-phase flow modellings of SCW. [ABSTRACT FROM AUTHOR]

• A multiphase projection-based particle method for flows of large density ratios and discontinuous density fields. • A computational algorithm on the basis of optimized particle shifting is incorporated for interface stabilization. • Validations and comparisons are conducted through several multiphase benchmark tests. • An extended version of an iterative shifting scheme is implemented and tested. • The present study portrays the robustness of particle shifting concept for multiphase particle-based simulations. A novel projection-based particle method is presented for simulation of multiphase flows characterized by large density ratios and discontinuous density fields at the phase interface. The method considers a multi-fluid continuous system and comprises of a specific computational algorithm utilizing the recently developed Optimized Particle Shifting (OPS [1]) scheme to maintain the regularity of particles at the phase interface and free-surface. The method is founded on an improved version of Moving Particle Semi-implicit (MPS [2]) as a projection-based particle method. A set of previously developed improved schemes are also adopted and hence the proposed method is referred to as improved MPS + OPS. Validations are made both qualitatively and quantitatively in terms of accuracy, energy conservation properties as well as convergence properties by consideration of several benchmark tests. [ABSTRACT FROM AUTHOR]

• Fully compressible model describing the conservation of mass, momentum and energy in SPH-ALE. • A micro jet is generated and hits the bubble during its compression near a wall. • A pressure wave is generated during the bubble collapse. • Two pressure peaks of high amplitude hit the wall during the bubble compression. This paper is motivated by the cavitation phenomenon, which occurs when bubbles collapse near a hydraulic machine surface. The bubble compression close to the wall has been addressed as the fundamental mechanism producing cavitation damage, whose general behavior is characterized by the emission of pressure waves and the formation of a micro jet. In order to simulate the collapse of a gas bubble in water, it is proposed a multiphase and compressible model developed in SPH-ALE. This model does not diffuse the interface and guarantees the continuity of normal velocity and pressure at the interface between both fluids, allowing it to deal with interfaces of simple contact. The model solves the mass, momentum and energy conservation equations of Euler system using an equation of state for each phase without phase change. The compressible model was validated through monodimensional configurations, such as shock tube test cases for monophase and multiphase flows. Bubble collapse simulations in 2D are presented highlighting the principle features, i.e. pressure waves and micro jets. Also, it is analyzed the effect of the initial distance between the bubble and the wall (H 0). Limitations and perspectives of SPH-ALE method on this particular subject are also discussed. [ABSTRACT FROM AUTHOR]

• An Isogeometric multi-phase flow formulation with surface tension using RBVMS and level-set method is proposed. • Superior accuracy IGA in mean curvature computation is demonstrated. • Comparison of IGA and FEM on level-set convection, mean curvature calculation and bubble rising dynamics is shown. • Merging processes of two bubbles under a free-surface is presented to show the capabilities of the proposed formulation. A novel multi-phase flow formulation using a level-set-based interface-capturing approach is proposed, focusing on addressing numerical challenges associated with the modeling of surface tension. The surface tension is handled through the continuum surface force model. The residual-based variational multiscale (RBVMS) formulation is employed to solve the coupled Navier–Stokes and level-set convection equations. The RBVMS formulation is discretized using either standard low-order finite elements, or Isogeometric Analysis (IGA) based on Non-Uniform Rational B-Splines (NURBS), which are higher-order accurate and smooth. The proposed method is applied to the simulation of 3D bubbles moving in viscous liquids with large density and viscosity ratios representative of common two-phase flow systems. The accuracy of the proposed method is assessed by comparing the results with analytical solutions, experimental data, and computational results, reported in the literature. In all cases IGA showed superior performance to standard finite elements; this superiority is attributed to the higher-order accuracy of IGA and its ability to directly and accurately compute, using smooth NURBS functions, the curvature term, which is a key ingredient the surface tension formulation. For single-bubble rising problems, the proposed approach produced accurate predictions of the terminal bubble shape, velocity and Reynolds number. The advanced nature of the new multi-phase flow formulation is demonstrated with a simulation of merging of two bubbles in the presence of a deforming free-surface. [ABSTRACT FROM AUTHOR]

Highlights • Conserved Allen–Cahn type multi-phase-field model is developed. • It can simulate the multiphase flow phenomena with an arbitrary number of phases. • It can accurately simulate the multiphase flow problems. Abstract The phase-field (PF) method is a method for interface tracking that can treat complex topological changes relatively easily because of its diffuse interface model. Therefore, as computational resources become increasingly powerful, it is a promising interface tracking method for multiphase flow problems. In this study, we developed a novel multi-PF (MPF) model for expressing flows that consist of an arbitrary number of phases. Here, we adopt the conservative Allen–Cahn (CAC) model instead of the Cahn–Hilliard model, which is often employed in multiphase flow problems, to reduce computational cost and increase the flexibility of the model for various problems. Six sets of two-dimensional simulations were performed to confirm the validity of the developed model for simulating the static and dynamic phenomena of the multiphase flow problem while conserving the volume of each phase. The results confirm that the developed CAC-type MPF model can accurately express the contact angle of a droplet placed on a solid substrate and the motion of bubbles interacting with liquid–liquid interfaces. [ABSTRACT FROM AUTHOR]

Highlighs • A novel weighting function for the fluid–particle interactions is proposed. • The relaxation parameter effect is avoided in the novel weighting function. • Parameters a = 50 and b = 0.01 are suggested for the proposed weighting function. • The smoothing nature of the proposed Bn is necessary for numerical stability. Abstract In order to improve the accuracy of existing immersed moving boundary method (IMBM) for the coupled discrete element lattice Boltzmann method, a novel weighting function for the fluid–particle interfacial interactions in IMBM is presented in this work. The flow is solved by the three-dimensional lattice Boltzmann method (LBM) D3Q15. The motions of particles are simulated by the discrete element method (DEM). The immersed moving boundary method is applied to resolve the momentum exchange between moving particles and fluids. The solid volume fraction of the fluid cell is calculated by the sphero-polyhedra method. The coupled IMBM–LBM–DEM is programmed based on the open source library Mechsys. The proposed method is validated by simulating flow past a stationary sphere, settling of a sphere and rebound of a spherical particle. These validations demonstrate the accuracy and reliability of this proposed method, which also has a good improvement over the original IMBM. Finally, effects of different parameters in the proposed weighting function are discussed and the suggested values a = 50, b = 0.01 are determined. This paper has implications for improving the ability to capture the fluid–particle interactions for a multiphase flow system. [ABSTRACT FROM AUTHOR]

Highlights • Smoothed Particle Hydrodynamics (SPH) model for thermo-capillary flow driven by gradients of the surface tension. • Continuum surface force (CSF) approach including Marangoni forces. • Convergence study for thermos-capillary flow. Abstract Interfacial-driven flows are important phenomena in many processes. In this article, we present a Smoothed Particle Hydrodynamics (SPH) model for thermo-capillary flow driven by gradients of the surface tension. The model is based on the continuum surface force (CSF) approach including Marangoni forces. An incompressible SPH approach using (i) density-invariant divergence-free (DIDF), (ii) corrected SPH and (iii) particle shifting approaches for multi-phase systems is used for accurate results. We carefully validate the proposed model using several test cases. First, we demonstrate the effects of corrected SPH and particle shifting approaches using Taylor-Green vortex. Then, we study single-phase flow problems to validate correct implementation of boundary conditions, momentum and energy balance using lid-driven cavity, diffusive transport problem, and buoyancy-driven cavity test cases. Afterward, we investigate different multi-phase flow problems to validate normal and tangential component of the surface tension. Finally, we apply the model to thermo-capillary rise of a droplet due to a temperature gradient. We present a convergence study and compare the results with their counterparts obtained from OpenFoam software as well as Finite Volume method (FVM) reference from literature. We demonstrate that the proposed model is very accurate for thermo-capillary flow. The simulation results of the current SPH approach will be available online for the community. [ABSTRACT FROM AUTHOR]

The high-order kinetic model for compressible multiphase flow is presented within the framework of the discrete Boltzmann method (DBM). Based on the Carnahan–Starling state equation, this model can describe the phase transition by introducing a source term of molecular interaction on the right-hand side of the Boltzmann equation. Meanwhile, the force term is incorporated to describe the external force. Through Hermite polynomial expansion, the equilibrium distribution function is expressed. Compared to the Navier–Stokes equations, the DBM provides more detailed and accurate information on both hydrodynamic and thermodynamic non-equilibrium effects. Finally, the model is verified through several typical benchmarks, including the liquid–vapor coexistence curve, free-falling process, shock wave, sound wave, thermal phase separation, and two-bubble oblique collision. [ABSTRACT FROM AUTHOR]

In the framework of the in-house code Fugu, a fully-coupled solver is developed for massively parallel simulations of three-dimensional incompressible multiphase flows. The linearized momentum and continuity equations arising from the implicit solution of the fluid velocities and pressure are solved simultaneously. The method uses a BiCGStab(2) (Dongarra et al., 1998) iterative solver with an original preconditioner for the velocity block and an approximation of the inverse of the Schur complement. This is achieved by using PFMG or SMG from HYPRE and an efficient sparse matrix–vector multiplication using the CSR storage format. The construction and the tracking of the interface separating the different involved phases is based on a conservative VOF method. Test cases, such as a spherical bubble rising in quiescent liquid and the free fall of a dense sphere, are performed to validate the models, especially in the presence of strong density and viscosity ratios between fluids. Other cases, such as the phase inversion, demonstrate the ability of the new fully-coupled solver to solve two-phase problems with more than 1 billion degrees of freedom with excellent scalability. • 3D fully coupled solver for multiphase flows based on one fluid model and VOF methods. • MPI parallel solver scaling until 10000 procs on more than 1 billion mesh cells. • Validated on various unsteady multiphase flows with high density and viscosity. [ABSTRACT FROM AUTHOR]

• Suitability of body force model for simulating pressure-difference-driven porous flows is identified by pore-scale simulations. • The body force model is suitable for most homogeneous porous structures for single-phase flows. • The body force model is not suitable for heterogeneous structures with preferential pathway. • The body force model leads to significant errors for multiphase flows even at a low C a. Pore-scale direct numerical simulation is an important tool for studying the flow of porous media nowadays. This work validates the suitability of body force model for simulating pressure-difference-driven porous flows in pore-scale simulations. The multi-relaxation time lattice Boltzmann method (MRT-LBM) with the color-gradient continuum-surface-force (CG-CSF) model is employed to calculate the absolute and relative permeability of randomly generated porous media. Results show that for single-phase flows, the relative errors are below 5% for most homogeneous porous structures while as high as 80% for structures with preferential paths. This study also reveals the pore-scale flow mechanisms and proposes a new heterogeneity parameter quantified by the standard deviation of the pressure at the boundary. For multiphase flows, errors of the body force model are significant at low C a due to irreversible phase distribution difference appearing at the early stages. The findings of this work could be applied to other transport processes in porous media. It is crucial to consider the structural heterogeneity and proper parameters when employing the body force model in pore-scale simulations. [ABSTRACT FROM AUTHOR]

Highlights • The hybrid model is capable of resolving various cavities in different length scales. • The new improvements avoid spurious pressure pulses and spurious vapour generation. • Consideration of bubble contribution in the Eulerian equations and mixture properties. • Better representation of the spatial distribution of Eulerian cavity after transition. Abstract Cavitating multi-phase flows include an extensive range of cavity structures with different length scales, from micro bubbles to large sheet cavities that may fully cover the surface of a device. To avoid high computational expenses, incompressible transport equation models are considered a practical option for simulation of large scale cavitating flows, normally with limited representation of the small scale vapour structures. To improve the resolution of all scales of cavity structures in these models at a moderate additional computational cost, a possible approach is to develop a hybrid Eulerian mixture -Lagrangian bubble solver in which the larger cavities are considered in the Eulerian framework and the small (sub-grid) structures are tracked as Lagrangian bubbles. A critical step in developing such hybrid models is the correct transition of the cavity structures from the Eulerian mixture to a Lagrangian discrete bubble framework. In this paper, such a multi-scale model for numerical simulation of cavitating flows is described and some encountered numerical issues for Eulerian–Lagrangian transition are presented. To address these issues, a new improved formulation is developed, and simulation results are presented that show the issues are overcome in the new model. [ABSTRACT FROM AUTHOR]

The importance of the two-phase flow model relies upon the correct simulation of specific problems in which the passive tracer model fails; however, the mathematical and numerical models need to be improved in order to reproduce fluid-solid particle interactions of greater complexity. Such is the case with regard to simulating erosion patterns suffered upon horizontal granular beds by means of a vertical water jet as shown here. Moreover, sequential platforms have proven to be insufficient in providing the required computational power needed to obtain fast and detailed simulations. In this paper, a fully parallel algorithm for a two-dimensional x / z two-phase Eulerian approach is presented and applied for the numerical solution of the erosion of sediment beds. The parallelization is designed by a row and column block domain decomposition technique using a distributed memory platform with Message Passing Interface (MPI). Arising from the numerical method, a Poisson problem for the pressure is solved at each time step. The discretization results in a non-symmetric variable-coefficient linear system which is solved using several parallel Successive Over-Relaxation (SOR) algorithms, including partitioning and coloring methods. The specification of the optimal relaxation parameter to achieve efficiency is found numerically. Results show that SOR methods achieve faster convergence rates and the simulation time achieves an order similar to that required for the typical, widely-used Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) method. The performances of the algorithms are evaluated in terms of speedup and efficiency. The results indicate that the parallel code significantly improves the results of the sequential calculation in general. [ABSTRACT FROM AUTHOR]

This paper extends a recently proposed multi-region based numerical wave tank (Martínez-Ferrer et al. [1]) to solve water entry problems in naval engineering. The original static linking strategy is developed to enable the dynamic coupling of several moving regions. This permits the method to deal with large-amplitude motions for structures slamming into water waves. A background grid and one or more component meshes are firstly generated to overlay the whole computational domain and the sub-domains surrounding the structures, respectively. During computation, the background mesh is fixed while the small grids move freely or as prescribed without deformation and regeneration. This effectively circumvents the large and often excessive error-prone dynamic deformation of a single-block mesh as well as the complex and time-consuming mesh regeneration. Test cases of dam breaking with and without obstacles are first conducted to verify the developed code by comparing the numerical solution against experimental data. Then the new code is used to solve prescribed and free-fall water entry problems. The obtained results agree well with experimental measurements and other computational results reported in the literature. [ABSTRACT FROM AUTHOR]

Micro-scale physiological fluid propulsion is often accomplished with arrays of beating cilia. It is well-known that cilia can spontaneously coordinate their beat patterns to form metachronal waves. While it is generally agreed upon that metachronal waves arise largely due to hydrodynamic coupling, their effects on fluid propulsion are not thoroughly explored. There are presently complex, nonlinear models where cilia motion mimics their internal mechanisms; however these models are often computationally challenging and expensive to perform. We therefore present a simplified computational model of a cilia array with the ability to spontaneously produce metachronal waves. Each cilium is modeled as a one-dimensional elastic structure immersed in a stratified, two-fluid configuration. This model is used to simulate in vitro artificial cilia. Our model treats the upper fluid as a high-viscosity Newtonian fluid. Our model shows that, in the presence of surface tension between the lower and upper fluid layers, the fluid velocity component perpendicular to the interface is suppressed. This suppression prevents the interface from deforming, leading to increased fluid flow along the cilia array and enhancing fluid transport. Conversely, in the absence of surface tension, the fluid velocity component perpendicular to the interface is unsuppressed. The interface becomes severely deformed, enlarging the fluid interface area, thus potentially enhancing diffusive mixing. We finally present a phase-space plot of viscosity ratio against surface tension, showing conditions under which fluid transport or mixing is enhanced. [ABSTRACT FROM AUTHOR]

This paper presents a new immersed boundary method for rigid particles of arbitrary shape and arbitrary density, which can be exactly zero. Especially in the latter case, the coupling of the fluid and the solid part requires special numerical techniques to obtain stability. Exploiting the direct forcing approach an algorithm with strong coupling between fluid and particles is developed, which is exempt from any global iteration between the fluid part and the solid part within a single time step. Starting point is a previously proposed method restricted to spherical particles [37]. It is proved that the coupling concept can be generalized to rigid particles with complex shapes, which is not obvious a priori . The extension requires various non-trivial methodological extensions, especially with respect to the angular motion of the particle. Using analytical techniques it is demonstrated that the implicit treatment of the coupling force in the equations of motion results in additional terms related to a surrounding numerical fluid layer. As a main improvement over other non-iterative methods the proposed scheme is unconditionally stable for the entire range of density ratios and particle shapes allowing large time steps, with Courant numbers around unity. To date, no other non-iterative coupling approach offers such a generality regarding fluid-particle interactions. In addition to the detailed description of the underlying methodology and its differences from other methods, the paper provides all modifications required to improve immersed boundary methods for particulate flows from weak to strong coupling. Furthermore, an extensive validation of the scheme for particles of different density ratios and shapes is presented. The accuracy of the method as well as the convergence behavior are assessed by systematic studies. [ABSTRACT FROM AUTHOR]

Hot spots ignition and shock to detonation transition modeling in pressed explosives is addressed in the frame of multiphase flow theory. Shock propagation results in mechanical disequilibrium effects between the condensed phase and the gas trapped in pores. Resulting subscale motion creates hot spots at pore scales. Pore collapse is modeled as a pressure relaxation process, during which dissipated power by the ‘configuration’ pressure produces local heating. Such an approach reduces 3D micromechanics and subscale contacts effects to a ‘granular’ equation of state. Hot spots criticity then results of the competition between heat deposition and conductive losses. Heat losses between the hot solid-gas interface at pore's scale and the colder solid core grains are determined through a subgrid model using two energy equations for the solid phase. The conventional energy balance equation provides the volume average solid temperature and a non-conventional energy equation provides the solid core temperature that accounts for shock heating. With the help of these two temperatures and subscale reconstruction, the interface temperature is determined as well as interfacial heat loss. The overall flow model thus combines a full disequilibrium two-phase model for the mean solid-gas flow variables with a subgrid model, aimed to compute local solid-gas interface temperature. Its evolution results of both subscale motion dissipation and conductive heat loss. The interface temperature serves as ignition criterion for the solid material deflagration. There is no subscale mesh, no system of partial differential equations solved at grain scale. The resulting model contains less parameter than existing ones and associates physical meaning to each of them. It is validated against experiments in two very different regimes: Shock to detonation transition, that typically happens in pressure ranges of 50 kbar and shock propagation that involves pressure ranges 10 times higher. [ABSTRACT FROM AUTHOR]

A first-order well-balanced finite volume scheme for the solution of a multi-component gas flow model in a pipe on non-flat topography is introduced. The mathematical model consists of Euler equations with source terms which arise from heat exchange, and gravity and viscosity forces, coupled with the mass conservation equations of species. We propose a segregated scheme in which the Euler and species equations are solved separately. This methodology leads to a flux vector in the Euler equations which depends not only on the conservative variables but also on time and space variables through the gas composition. This fact makes necessary to add some artificial viscosity to the usual numerical flux which is done by introducing an additional source term. Besides, in order to preserve the positivity of the species concentrations, we discretize the flux in the mass conservation equations for species, in accordance with the upwind discretization of the total mass conservation equation in the Euler system. Moreover, as proposed in a previous reference by the authors, [5], the discretizations of the flux and source terms are made so as to ensure that the full scheme is well-balanced. Numerical tests including both academic and real gas network problems are solved, showing the performance of the proposed methodology. [ABSTRACT FROM AUTHOR]

In order to present velocity and pressure spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material gas flows (when the specific heats ratio is variable), a quasi-conservative numerical model has been proposed. However, designing a consistent numerical algorithm, especially using the high-order characteristic flux-split based finite-difference method (CFS-FDM) for this model, is still an open question. In this study, a systematical analysis of previous algorithms of the consistent implementation of the high-order CFS-FDM for such flows is performed, and reasons of special treatments in these algorithms are revealed. Based on this analysis, a new general numerical methodology that successfully avoids any special treatments as those required in previously reported algorithms, is derived. In this new algorithm, we rewrite the non-conservative term as a conservative term with a source term containing the velocity divergence. By consistently treating the advection velocity in the conservative term and the velocity divergence in the source term by imposing a new additional criterion, specifically, that a multicomponent-fluid algorithm should have the ability of maintaining a pure single-fluid, we finally derive a new general algorithm that does not need any special treatment, and is very convenient to implement. The results of some benchmark tests show that the final algorithm not only maintains the velocity and pressure equilibria, but is also suitable for problems regarding the interaction of interfaces and strong shock and rarefaction waves. [ABSTRACT FROM AUTHOR]

In this work, an alternate level-set-based approach is presented that applies uniformly to compressible and incompressible multiphase flows. Fundamental to this work, is the development of analytic transformations from a signed-distance function to species-mass conservation variables. Such transformations can be used to highlight compressible flow difficulties for level set methods, and develop interfacial reinitialization procedures based on different primitive variables. The proposed all-Mach method is based on preserving signed-distance functions within the context of a species-mass conservation equation to evolve the interface, and includes several reinitialization procedures that maintain the spirit of the signed distance function. In addition, we explore hybrid level-set reinitialization procedures that handle sub-grid-scale interfacial breakup. The model is demonstrated on concepts relevant to high-speed marine vehicles based on supercavitation, where a gaseous cavity surrounds a moving vehicle. Results indicate that the present algorithm preserves higher-order numerics, performs well on several incompressible and compressible validation cases, and extends to unsteady, three-dimensional flow. [ABSTRACT FROM AUTHOR]

We present a regularized version of the color gradient lattice Boltzmann (LB) scheme for the simulation of droplet formation in microfluidic devices of experimental relevance. The regularized version is shown to provide computationally efficient access to capillary number regimes relevant to droplet generation via microfluidic devices, such as flow-focusers and the more recent microfluidic step emulsifier devices. [ABSTRACT FROM AUTHOR]

A method is proposed for modelling contact line dynamics in volume-of-fluid frameworks using a common and robust ghost-cell immersed boundary method in 2D. The method implements a contact line model based on the CELESTE method, used in conjunction with a CICSAM scheme capable of handling multiphase flows in which the phases have large variations in their physical properties. The ability of the model to resolve contact lines on both planar and curved geometries is demonstrated. It is also shown that the model maintains good mass conservation. Dynamic cases studied include a planar water droplet impact onto a cylinder, as well as a planar droplet penetration into a bank of cylinders with varying hydrophobicity. [ABSTRACT FROM AUTHOR]

Probability density functions (PDF) and the relevant methods have been widely used to describe non-linear phenomena in the realm of turbulence modelling and CFD. In order to solve PDF transport equations, the main trend of previous studies rely on Monte Carlo method with Lagrangian particle tracking. However, as with any Lagrangian based approach, the scalability of the parallelized simulations of such method is less than satisfactory. An Eulerian stochastic field model has been presented recently by Dumond et al. [1] to simulate cavitating flows. Their model uses a fully compressible density based solver. Here we present an adapted version using an iso-thermal cavitation model adopting the homogeneous mixture assumption in a pressure based flow solver which is more relevant to engine simulations. A PDF method is used to represent a distribution of vapour volume fractions, based on which the Eulerian stochastic field (ESF) method is applied to perform a three-dimensional large eddy simulation (LES) of the cavitation phenomena inside an academic fuel injector configuration. The numerical model is based on a volume of fluids approach and coupled with a pressure based solver for the flow field, and is implemented in the framework of the open source C++ toolbox OpenFOAM. The result of the ESF simulation is compared against that from a typical single volume fraction solver for validation. Vortex structures and its correspondence to cavitation are shown, and the behaviour of the PDF at different probe locations at different times are acquired to demonstrate the potential of the ESF model in capturing both transient and stochastically steady cavitation. [ABSTRACT FROM AUTHOR]

The Volume of Fluid method is extensively used for the multiphase flows simulations in which the interface between two fluids is represented by a discrete and abruptly-varying volume fractions field. The Heaviside nature of the volume fractions field presents an immense challenge for the accurate computation of the interface curvature and induces the spurious velocities in the flows with surface-tension effects. A 3D hybrid approach is presented combining the Convolution and Generalized Height Function method for the curvature computation. The volumetric surface tension forces are computed using the balanced-force continuum surface force model. It provides a high degree of robustness at lower grid resolutions with first-order convergence and high accuracy at higher grid resolutions with second-order convergence. The present method is validated for several test cases including a stationary droplet, an oscillating droplet and the buoyant rise of gas bubbles over a wide range of Eötvös ( Eo ) and Morton ( Mo ) numbers. Our computational results show an excellent agreement with analytical/experimental results with desired convergence behavior. [ABSTRACT FROM AUTHOR]

Hot spots ignition and shock to detonation transition modeling in pressed explosives is addressed in the frame of multiphase flow theory. Shock propagation results in mechanical disequilibrium effects between the condensed phase and the gas trapped in pores. Resulting subscale motion creates hot spots at pore scales. Pore collapse is modeled as a pressure relaxation process, during which dissipated power by the ‘configuration’ pressure produces local heating. Such an approach reduces 3D micromechanics and subscale contacts effects to a ‘granular’ equation of state. Hot spots criticity then results of the competition between heat deposition and conductive losses. Heat losses between the hot solid-gas interface at pore's scale and the colder solid core grains are determined through a subgrid model using two energy equations for the solid phase. The conventional energy balance equation provides the volume average solid temperature and a non-conventional energy equation provides the solid core temperature that accounts for shock heating. With the help of these two temperatures and subscale reconstruction, the interface temperature is determined as well as interfacial heat loss. The overall flow model thus combines a full disequilibrium two-phase model for the mean solid-gas flow variables with a subgrid model, aimed to compute local solid-gas interface temperature. Its evolution results of both subscale motion dissipation and conductive heat loss. The interface temperature serves as ignition criterion for the solid material deflagration. There is no subscale mesh, no system of partial differential equations solved at grain scale. The resulting model contains less parameter than existing ones and associates physical meaning to each of them. It is validated against experiments in two very different regimes: Shock to detonation transition, that typically happens in pressure ranges of 50 kbar and shock propagation that involves pressure ranges 10 times higher. [ABSTRACT FROM AUTHOR]

This paper introduces a three-phases model based on the finite element method to simulate the generation and propagation of landslide-generated impulse waves, and this model can be employed to predict and prevent wave-induced hazards. The fluid-like landslide mass is treated as a non-Newtonian viscoplastic fluid. The motion of landslides, water and air is modelled by the incompressible Navier–Stokes equations and the interfaces between these three phases are captured with the n -phases improved conservative level set method which can preserve mass and provide precious interface parameters, including normals and curvatures. The conservative feature of this method is proven by the three-phases Zalesak slotted disk test case. This method is then adopted to simulate the impulse wave generated by the Lituya Bay landslide and the current outputs are compared with other existing results. Finally, this verified model is utilized to model the impulse waves generated by the Halaowo landslide near the Xiangjiaba Dam in the Jinsha River and the results could provide references for further protective activities. [ABSTRACT FROM AUTHOR]

Spurious currents are often observed near curved interfaces in multiphase simulations based on diffuse interface methods. These unphysical phenomena negatively affect both computational accuracy and stability. In this paper, the origin and suppression of spurious currents are investigated using the multiphase lattice Boltzmann method driven by a chemical potential. Both the difference error and insufficient isotropy of the discrete gradient operator give rise to directional deviations in the nonideal force, leading to spurious currents. Nevertheless, a high-order finite difference scheme produces far more accurate results than a high-order isotropic difference scheme. We compare several finite difference schemes that have different levels of accuracy and resolution. When a large proportional coefficient is used, the transition region is narrow and steep, and the resolution of the finite difference scheme provides a better indication of the computational accuracy than the formal accuracy. Conversely, for a small proportional coefficient, the transition region is wide and gentle, and the formal accuracy of the finite difference gives a better indication of the computational accuracy than the resolution. Numerical simulations show that the spurious currents calculated in the three-dimensional situation are highly consistent with those in two-dimensional simulations; in particular, the two-phase coexistence densities calculated by the high-order accuracy finite difference scheme are in excellent agreement with the theoretical predictions of the Maxwell equal-area construction down to a reduced temperature of 0.2. • Spurious currents is investigated in multiphase lattice Boltzmann method. • The discrete gradient is calculated by a finite difference scheme with high computational accuracy instead of the traditional isotropic difference scheme. • This scheme satisfies thermodynamic consistency. • This scheme effectively suppresses the spurious currents to a lower level. Even at a temperature of 0.6, the magnitude of the spurious currents is only 10−5. [ABSTRACT FROM AUTHOR]

In the late 90's and early 2000's the concept of a discrete H theorem and Lyapunov functionals as a way to ensure stability of lattice Boltzmann solvers was a shift of paradigm in the construction of discrete kinetic solvers and opened the door for new discussions and perspectives on the matter. The entropic construction proposed to reorganize the relaxation collision operator by changing both the equilibrium attractor and relaxation process by introducing a discrete entropy functional and enforcing an H-theorem. The concept has proven to be effective in stabilizing lattice Boltzmann solvers in a variety of different area of applications ranging from isothermal weakly compressible, to fully compressible and multi-phase flows. Here we review basic building blocks of the entropic lattice Boltzmann method and discuss its extension to multiphase and compressible flows. [ABSTRACT FROM AUTHOR]

This paper concerns the numerical study of a class of box-relaxation (coupled) smoothers for multigrid solvers applied to the variable viscosity Stokes problem. In particular, we address the case of multi-phase flows of non miscible fluids with a high viscosity contrast, which are particularly challenging to solve using iterative methods and need robust preconditioning strategies. Three variants of box-relaxation are presented. These are defined based on the algebraic structure of the discrete operators only and therefore can be be compatible, in principle, with most of discretization techniques. Several tests are carried out to assess the robustness of the proposed approach against the varying viscosity contrast (up to 10 7 ), mesh size and mesh stretching factor. Finally, as a practical application, the box-relaxation smoother is used in the framework of flow simulation for multi-layer coextrusion of polymeric fluids. [ABSTRACT FROM AUTHOR]

One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time Discontinuous Galerkin (DG) Finite Element method with h -adaptivity to improve the efficiency of one-dimensional multiphase flow simulations. For smooth initial boundary value problems we show that the DG method converges with the theoretical rate and that the growth rate and phase shift of small, harmonic perturbations exhibit superconvergence. We employ two techniques to accurately and efficiently represent discontinuities. Firstly artificial diffusion in the neighbourhood of a discontinuity suppresses spurious oscillations. Secondly local mesh refinement allows for a sharper representation of the discontinuity while keeping the amount of work required to obtain a solution relatively low. The proposed DG method is shown to be superior to FV. [ABSTRACT FROM AUTHOR]