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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]

• 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 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]

• 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]

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]

In this paper the characteristics of the primary breakup of a liquid jet is analyzed numerically. We applied the Volumes of Fluids (VOF) approach utilizing the Direction Averaged Curvature (DAC) model, to estimate the interface curvature, and the Direction Averaged Normal (DAN) model, to propagate the interface. While being used for the first time to predict liquid atomization, this methodology showed a high accuracy. The influence of varying the fluid properties, namely liquid-gas density and viscosity ratio, and injection conditions is discussed related to the required grid resolution. Resulting droplet sizes are compared to distributions obtained through the One-Dimensional Turbulence (ODT) model. [ABSTRACT FROM AUTHOR]

A flow model is derived for the numerical simulation of multi-phase flows with phase transition. The model arises from the classical multi-component Euler equations, but is associated to a non-classical thermodynamic closure: each phase is compressible and evolves in its own subvolume, with phases sharing common pressure, velocity and temperature, leading to non-trivial thermodynamic relations for the mixture. Phase transition is made possible through the introduction of Gibbs free energy relaxation terms in the equations. Capillary effects and heat conduction – essential in boiling flows – are introduced as well. The resulting multi-phase flow model is hyperbolic, valid for arbitrary density jumps at interfaces as well as arbitrary flow speeds. Its capabilities are illustrated successively through examples of nozzle induced cavitation, a high-speed evaporating liquid jet, and heated wall induced boiling. [ABSTRACT FROM AUTHOR]

In this paper, we present an adaptive implementation of the distributed Lagrange multiplier (DLM) immersed boundary (IB) method on multilevel collocated grids for solving single- and multiphase fluid–structure interaction (FSI) problems. Both a non-subcycling time advancement scheme and a subcycling time advancement scheme, which are applied to time-march the composite grid variables on a level-by-level basis, are presented; these schemes use the same time step size and a different time step size, respectively, on different levels. This is in contrast to the existing adaptive versions of the IB method in the literature, in which coarse- and fine-level variables are simultaneously solved and advanced in a coupled fashion. A force-averaging technique and a series of synchronization operations are constructed to achieve excellent momentum and mass conservation across multiple levels of grid hierarchy. We demonstrate the versatility of the present multilevel framework by simulating problems with various types of kinematic constraints imposed by structures on fluids, such as imposing a prescribed motion, free motion, and time-evolving shape of a solid body. The DLM method is also coupled to a robust level set method-based two-phase fluid solver to simulate challenging multiphase flow problems, including wave energy harvesting using a mechanical oscillator. The capabilities and robustness of the computational framework are validated against a variety of benchmarking single-phase and multiphase FSI problems from the literature, which include a three-dimensional swimming eel model to demonstrate the significant speedup and efficiency that result from employing the present multilevel subcycling FSI scheme. • Built an adaptive distributed Lagrangian multiplier (DLM) framework for fluid–structure interaction (FSI) problems. • Both the subcycling and non-subcycling methods are included in the multi-level collocated grid. • Designed a force-averaging scheme and synchronization operations for momentum and mass conservation. • The DLM method is coupled to a robust level set method to simulate multiphase flows problems. • Validated the capability, robustness, and efficiency of the computational framework. [ABSTRACT FROM AUTHOR]

Compressible interfacial multiphase flows (CIMF) are essential to different applications, such as liquid fuel injection in supersonic propulsion systems. Since high-level details in CIMF are often difficult to measure in experiments, numerical simulation is an important alternative to shed light on the unclear physics. A direct numerical simulation (DNS) of CIMF will need to rigorously resolve the shock waves, the interfaces, and the interaction between the two. A novel numerical method has been developed and implemented in the present study. The geometric volume-of-fluid (VOF) method is employed to resolve the sharp interfaces between the two phases. The advection of the density, momentum, and energy is carried out consistently with VOF advection. To suppress spurious oscillations near shocks, numerical diffusion is introduced based on the Kurganov–Tadmor method in the region away from the interface. The contribution of pressure is incorporated using the projection method and the pressure is obtained by solving the Poisson–Helmholtz equation, which allows the present method to handle flows with all Mach numbers. The present method is tested by a sequence of CIMF problems. The simulation results are validated against theories, experiments, and other simulations, and excellent agreement has been achieved. In particular, the linear single-mode Richtmyer–Meshkov instabilities with finite Weber and Reynolds numbers are simulated. The simulation results agree very well with the linear stability theory, which affirms the capability of the present method in capturing the viscous and capillary effects on shock-interface interaction. • A method is established for simulation of compressible interfacial multiphase flows. • Advection of conservative variables is consistent with VOF advection of interface. • Numerical diffusion based on the central upwind scheme is introduced to suppress spurious oscillations. • Accurately capturing shock interaction with sharp interfaces with surface tension. • Validation against linear Richtmyer–Meshkov instability theory for finite Weber and Reynolds numbers. [ABSTRACT FROM AUTHOR]

Highlights: [•] A Lattice Boltzmann Method (LBM) for the simulation of multiphase flows with high density ratios. [•] Viscosity included as part of the LBM particle distribution functions (PDFs). [•] No non-physical terms appear in any of the equations. [•] Efficiently GPGPU implementation, 10–100 times faster than for a single CPU. [•] Validation for a number of increasingly demanding, analytical and numerical, benchmark problems. [Copyright &y& Elsevier]

Abstract: We propose a high order diffuse interface method for dealing with compressible multiphase flows with interfaces. This scheme is based on the discontinuous Galerkin formulation of Franquet and Perrier . As it is linear, this scheme is oscillating, so that the volume fraction can become negative or greater than 1. For stabilizing it, the maximum preserving limiter introduced in Zhang et al. (2012) is used. The scheme is applied to the computation of a Rayleigh–Taylor instability. [Copyright &y& Elsevier]

Abstract: An improved model for simulation of phase transitions and single-component multiphase flows by lattice Boltzmann method is proposed and developed in this paper. It is shown that both the scheme for the interparticle interaction force term and the method of incorporating the force term are important for obtaining accurate and stable numerical results for simulations of single-component multiphase flows. A new scheme for the force term is proposed and simulation results of several non-ideal equation of state suggest that the proposed scheme can greatly improve the coexistence curves. Among several methods of incorporating the force term, the exact difference method is shown to have better accuracy and stability. Furthermore, it avoids the unphysical phenomenon of relaxation time dependence. Compared with existing models, the proposed model, consisting of the new force term scheme together with the exact different method to incorporate the force term, can give more accurate and stable numerical results in a wider temperature range with the spurious currents greatly reduced. Droplet motion and coalescence processes on surfaces with wettability gradients are numerically investigated based on the newly proposed model. The velocity field and mechanism of droplet motion are illustrated in details. [Copyright &y& Elsevier]

Abstract: A global methodology dealing with fictitious domains of all kinds on curvilinear grids is presented. The main idea is to transform the curvilinear framework and its associated elements (velocity, immersed interfaces…) into a Cartesian grid. On such grids, many operations can be performed much faster than on curvilinear grids. The method is coupled with a Thread Ray-casting algorithm which works on Cartesian grids only. This algorithm computes quickly the Heaviside function related to the interior of an object on an Eulerian grid. The approach is also coupled with an immersed boundary method (L 2-penalty) or with phase advection methods such as VOF–PLIC, VOF–TVD, Front-tracking or Level-set approaches. Applications, convergence and speed tests are performed for shape initializations, immersed boundary methods, and interface tracking. [Copyright &y& Elsevier]

Free surfaces and fluid interfaces are encountered in a wide variety of gas-liquid configurations. Although many numerical approaches exist to solve such flows, there is still a need for improved simulation methods. Recently, a new efficient geometric VoF method for general meshes, called isoAdvector, was implemented in OpenFOAM®. More recently, the isoAdvector method was significantly improved by introducing a variant using a reconstructed distance function (RDF) in the interface reconstruction step. Elementary quantitative benchmarks are essential for validation and comparison of interfacial solvers. We present here three benchmarks results that were used for validation of the original and new variant of the isoAdvector method. Comparisons are made with reference data and OpenFOAM® VoF original solver, interFoam, employing the MULES limiter. The first case is the static bubble under zero gravity. The RDF reconstruction method demonstrates better prediction of the interface curvature, pressure jump between the phases and strong reduction of the spurious currents. The second and third validation cases are single rising bubbles in a quiescent liquid, with a spiraling path for the third case. Either on hexahedral or tetrahedral grids, the RDF reconstruction method demonstrates a better behavior. [ABSTRACT FROM AUTHOR]

• 1st effort of its kind to develop machine learnt surrogate models for multiphase flows. • Model predicts gaseous and spray dynamics in both space and time. • Uncertainty quantified inherently due to use of Bayesian inference based algorithm. • Speedup up to 8000 achieved with errors between truth and surrogate model under 16%. This study focuses on the development of a theoretical framework and corresponding algorithms to establish spatio-temporal surrogate models for multiphase flow processes using Gaussian process (GP) based machine learning technique trained by direct numerical simulation (DNS) data. The training (and testing) datasets are obtained by solving the incompressible form of the Navier Stokes equations with surface tension in an Eulerian reference frame. The liquid-gas interfacial evolution is resolved using a volume-of-fluid (VOF) interface capturing method. The overall framework proceeds in four steps: 1) design of experiments study to identify the training and testing points and generation of corresponding datasets using DNS calculations; 2) dimensionality reduction using proper orthogonal decomposition; 3) Gaussian process regression (supervised training) over the reduced training dataset over the entire range of operating conditions under consideration; and 4) Galerkin reconstruction and error quantification by comparing the emulated flowfields (at test conditions) with the testing dataset. The machine learning framework predicts both the spatial basis-functions and the time-coefficients, thus, predicting the entire flowfield in time and space. The capabilities of the algorithm are demonstrated for two canonical flow configurations: 1) flow over a circular cylinder for a range of Reynolds numbers from 10 to 200; and 2) diesel jet injected into a quiescent nitrogen environment at chamber pressure of 30 atm and room temperature conditions, and injection velocities from 10 to 55 m/s, corresponding to a range of gas-based Weber numbers from 11.5 to 348. The emulations from the learned GP algorithm show excellent agreement with high-fidelity numerical data for test conditions; average error (in both space and time) at the testing point of Re = 185 for the flow over cylinder case is 4.4%, and for the diesel jet injection configuration at a testing point corresponding to velovity of 22.5 m/s is found to be 15.5%. The tip penetration location of the diesel jet is predicted within 2.5% of the DNS calculations. Corresponding to these two representative test points, speedup of 256 and 8000 is achieved for flow over cylinder and diesel jet atomization configurations, respectively. This paper represents the first effort of its kind on the development of a general machine learning framework to predict multiphase flows. [ABSTRACT FROM AUTHOR]