Search

A new volume of fluid (VOF) based two-phase flow solver has been developed that has been parallelized for general purpose graphical processor units (GPGPU). Incompressible Navier–Stokes equation is explicitly solved using finite volume method on a 2-D Cartesian grid. The pressure Poisson equation is solved on the GPU in conjunction with the geometric multigrid method. This solver performance is established by validating it against standard benchmark test cases. Furthermore, the solver acceleration is determined by comparing it with the serial version of the code. The solver was then used to study the primary jet breakup of a 2-D planar liquid jet due to a co-flowing gas stream. The effect of liquid to gas phase velocity ratio on jet breakup was investigated. [ABSTRACT FROM AUTHOR]

Numerical investigations of two-phase flows in anisotropic porous media have been conducted. In the flow model, the permeability has been considered as a full tensor and is implemented in the numerical scheme using the multipoint flux approximation within the framework of finite difference method. In addition, the experimenting pressure field approach is used to obtain the solution of the pressure field, which makes the matrix of coefficient of the global system easily constructed. A number of numerical experiments on the flow of two-phase system in two-dimensional porous medium domain are presented. In this work, the gravity is included in the model to capture the possible buoyancy-driven effects due to density differences between the two phases. Different anisotropy scenarios have been considered. From the numerical results, interesting patterns of the flow, pressure, and saturation fields emerge, which are significantly influenced by the anisotropy of the absolute permeability field. It is found that the two-phase system moves along the principal direction of anisotropy. Furthermore, the effects of anisotropy orientation on the flow rates and the cross flow index are also discussed in the paper. [ABSTRACT FROM AUTHOR]

In this work we develop, test and apply a height-function-based numerical code for the simulation of multiphase magnetic fluids. New hierarchical height function algorithms for interface normal and curvature (Bornia et al., 2011) are adapted and integrated into the Volume of Fluid component of our Navier–Stokes–Maxwell code for magnetic fluids and charge-free quasi-static magnetic fields. Accuracy and convergence results are presented for highly elongated ellipses characteristic of magnetic fluids, for static non-magnetic fluid droplets, and for magnetic fluid droplets elongated by an imposed uniform field. The code is applied to Magnetic Drug Targeting to demonstrate the response of magnetically controlled fluid regions to an imposed quadratic flow profile in a model vein. [ABSTRACT FROM AUTHOR]

A numerical method of initializing cell volume fraction demarcated by implicitly defined fluid interfaces is presented. Each cell of the computational domain is examined for the presence of the reference phase. When a cell is not full or empty, limits are found that allow volume fraction to be computed by numerical integration. The method enlists a number of algorithms including root finding and minimum search on an oriented segment, a preconditioned conjugate gradient minimum search on a cell face and a double Gauss–Legendre integration with a variable number of nodes, among others. Practical multi-phase fluid examples in two- and three-dimensions are presented to demonstrate the accuracy and robustness of the method. [ABSTRACT FROM AUTHOR]

In this paper, a multi-component lattice Boltzmann method (LBM) with different lattice speeds and multiple linearized collision terms is improved. The molecular weights, viscosities of each component and the diffusivities can be tuned separately. An exact calculation for relaxation times of the cross-collision terms is derived, which makes the model to be consistent with the Stefan–Maxwell equations. The derivation also demonstrates that the tuning-molecular-weight strategy is only available for the ternary diffusion. The expressions of the fluxes and the boundary conditions are proposed. A simulation of the one-dimensional diffusion demonstrates that the second-order interpolation is better than the first-order one to deal with the different lattice speed. The simulation of Couette flow shows that the model behaves like a single fluid with high Schmidt number, and the components tend to flow independently with small Schmidt number. The model is validated by the simulation of one-dimensional diffusion and two-dimensional opposed jet flow, where the LBM results coincide well with the results of the Stefan–Maxwell equations. Finally, the diffusion in a porous media is simulated as an example of the application of the model. This lattice Boltzmann model is suitable for simulating multi-component convection–diffusion problems with complex boundary conditions. [ABSTRACT FROM AUTHOR]

• The overall volume conservation equation of phase fractions is coupled in the decoupling procedure of velocity and pressure and naturally guaranteed. • The boundedness of the phase fractions is guaranteed both by 0 and 1 in the proposed method. • The singular problem of momentum equation in the Eulerian multi-fluid model and corresponding solutions are discussed. The study aims to present a convenient but practical method to guarantee the boundedness and conservation of phase fractions in the Eulerian multi-fluid model. The established Eulerian multi-fluid model is based on the finite volume method and implemented in the platform of OpenFOAM-v2012, which is an open-source software. It is completely unnecessary to employ any reconstruction techniques or rewrite the phase continuity equations to maintain the boundedness and conservation of phase fractions in the proposed method. The advection flux of the phase continuity equation is constructed within the coupling procedure of velocity and pressure and explicitly evaluated when solving the phase continuity equation. The upwind interpolation of the phase fraction is carried out before constructing the pressure equation; thus, the advection flux of the phase continuity equation could be corrected by the pressure equation for boundedness and conservation consideration. Those unique treatments only slightly differ from the standard solution procedure, but the boundedness and conservation could be naturally guaranteed. The proposed method is verified by two test cases, including the phase separation and the two-phase upward flow, to demonstrate the boundedness, conservation, and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

A continuous adjoint method is developed for design optimization in multiphase flow based on a homogeneous multiphase mixture model. The mixture model consists of variable-density mass and momentum equations and uses a barotropic equation of state for the density that depends on only the local static pressure and the vapor pressure of the liquid. In that case, the primary equations are homogeneous, and a conventional hybrid multistage explicit method based on central differencing and second- and fourth-order scalar artificial dissipation can be applied to solve both the primary and adjoint systems. Results are presented for both surface- and volume-based vapor minimization cost functions for a two-dimensional cavitating hydrofoil in which the geometry is parameterized using B-splines. The cost function gradients computed using the adjoint method are shown to compare well with gradients computed using the complex-step method. [ABSTRACT FROM AUTHOR]

As energy densities in electronic devices rapidly increase, improved two-phase microchannel heat exchanger designs are of great interest. Similarly, with the implementation of phase separation as a method of flow manipulation in microdevices, understanding the flow dynamics of multiple phases in microchannels is vital. However, experimental studies have thus far shown a great deal of variety in the flow patterns and instabilities that develop at the microscale level. These phenomena are further complicated by the presence of multiple chemical components. Thus, numerical techniques capable of simulating such flow regimes are desirable. The lattice Boltzmann method (LBM) is gaining traction as a powerful approach to fluid flow simulation due to its ability to capture interfacial dynamics without complex interface tracking algorithms. However, existing approaches are currently inadequate for thermal flows with multiple components and multiple phases. In this work, an analysis of the stability region of the interparticle interaction parameters in a multiphase, immiscible, multicomponent, isothermal model is conducted. Informed by this analysis, a multiphase, immiscible, multicomponent, thermal (MPiMC-T) model is constructed using a density-weighted coupling of macroscopic properties. Validation of the model is performed using a static thermal conduction simulation and a steady-state droplet simulation. Conservation properties are maintained and physical consistency is met across component grids in the immiscible limit. Furthermore, a reduction of spurious currents is obtained utilizing the multicomponent framework. [ABSTRACT FROM AUTHOR]

The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It provides a natural framework for treating the surfactant concentration equation, which is solved locally on each segment. An accurate numerical method for the coupled interface/surfactant system is given. The system is coupled to the Navier-Stokes equations through the immersed boundary method, and we discuss the issue of force regularization in wetting problems, when the interface touches the boundary of the domain. We use the method to illustrate how the presence of surfactants influences the behavior of free and wetting drops. [ABSTRACT FROM AUTHOR]

A two-fluid AUSM+-up numerical flux function with the exact (Godunov) Riemann solver for the stratified flow model concept by Chang et al. (2007) has been extended for simple and robust computations of compressible multiphase flows. The present method replaces the Godunov part with the HLLC approximate Riemann solver with no-iteration procedure in a very simple manner: This two-fluid HLLC has been inspired by the work by Hu et al. (2009), but used in a totally different way. Numerical tests demonstrate that the present two-fluid AUSM+-up is, if only velocity and pressure in the middle zone are computed by HLLC, as robust as the original, Godunov-combined AUSM+-up, despite being free from iterations and convergence criteria. [ABSTRACT FROM AUTHOR]

Highlights: [•] Discretizations for non-conservative terms with a simple HLLC scheme are derived. [•] TVD Runge–Kutta method is implemented with properly sequenced operator splitting. [•] A special procedure for block synchronization without exiting a kernel is proposed. [Copyright &y& Elsevier]

Highlights: [•] A pressure-based scheme for compressible two-phase flows is presented. [•] We use multiple pressure variables for the compressible–incompressible transition. [•] The material interface is resolved and tracked by the level set method. [•] The approach is free of spurious oscillations in the vicinity of the material interface. [•] The scheme is able to simulate the propagation of pressure waves in gases and liquids. [Copyright &y& Elsevier]

Highlights: [•] Simulation of interactions between moving rigid bodies and two-fluid flows. [•] GPU-accelerated multiphase flow solver for flows of arbitrarily large density ratios. [•] Fluid–solid interaction is captured by using the fictitious domain method. [•] The VOF method captures the evolution of interfaces in the three-phase system. [•] Interfaces in the three-phase cells are reconstructed and triple points are captured. [ABSTRACT FROM AUTHOR]

Highlights: [•] The MRT R–K LBM ensures better numerical stability and reduces spurious currents. [•] The non-equilibrium bounce back is extended to two-phase boundary condition. [•] Three typical flow patterns for immiscible displacement in porous media are obtained. [•] The first time to obtain a completed ‘M–Ca’ phase-diagram using LBM in literature. [Copyright &y& Elsevier]

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]

Highlights: [•] Multiphase LBM model is employed. [•] Coupling of reaction and hydrodynamics using LBM. [•] Flow around a droplet is simulated. [•] Mean field deterministic and kinetic Monte Carlo are used for reaction kinetics. [Copyright &y& Elsevier]

Highlights: [•] We consider compression of a cylindrical gas cavity by an imploding molten lead shell. [•] We study development of Richtmyer–Meshkov instability at liquid–gas interface. [•] Compression efficiency may be affected because of initial perturbations at the interface. [•] Strong asymmetry in development of ‘spikes’ and ‘bubbles’ has been observed. [•] Formation of narrow molten lead jets has been observed under a range of initial perturbations. [Copyright &y& Elsevier]

Highlights: [•] A compressible reactive flow solver is developed and thoroughly verified. [•] Supersonic combustion is studied in canonical conditions. [•] Special emphasis is placed on ignition and flame stabilization processes. [Copyright &y& Elsevier]

Highlights: [•] Improve LBM based color-model to simulate multiphase flow of binary fluid mixture with high density contrast. [•] Allow application of color-model for solving buoyancy dependent problems. [•] Demonstrate the robustness of proposed modification for range of problems. [•] Demonstrate the verification of proposed modification against benchmark problems in multiphase flow modeling. [Copyright &y& Elsevier]

Highlights: [•] A new interface-capturing method is proposed for compressible multicomponent flows. [•] A high-order central difference scheme is applied. [•] Consistent numerical diffusion terms are analytically derived. [•] Pressure, velocity, and temperature equilibriums at interfaces are maintained. [•] Several one- and two-dimensional problems are used to verify the proposed method. [Copyright &y& Elsevier]

Highlights: [•] Arbitrary-Lagrangian–Eulerian (ALE) finite volume schemes for non-linear non-conservative hyperbolic systems. [•] High order accurate path-conservative Lagrangian finite volume schemes. [•] WENO reconstruction on moving unstructured meshes. [•] Applications to the Baer–Nunziato model of compressible multiphase flows with stiff relaxation. [•] Very sharp resolution of material interfaces. [ABSTRACT FROM AUTHOR]

Highlights: [•] Analysis of VOF method for surface tension dominated multiphase flow simulations. [•] Providing guidelines for optimal computational settings. [•] Analysis of optimal balance between interface sharpness and parasitic currents. [•] Experimentally documented benchmarks for modeling bubble/droplet microfluidics. [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]

In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy sources. We derive three equivalent formulations for the proposed model. The first formulation consists of balance equations for partial densities, the mixture momentum, the mixture total energy, and phase volume fractions. The second formulation is symmetric and obtained by replacing the equations for the mixture total energy and volume fractions in the first formulation with balance equations for the phase total energy. Replacing one of the phase total energy equation of the second formulation with the mixture total energy equation gives the third formulation. All the three formulations assume velocity and pressure equilibrium across the material interface. These equivalent forms provide different physical perspectives and numerical conveniences. Temperature equilibration and continuity across the material interfaces are achieved with the instantaneous thermal relaxation. Temperature equilibrium is maintained during the heat conduction process. The proposed models are proved to respect the thermodynamical laws. For numerical solution, the model is split into a hyperbolic partial differential equation (PDE) system and parabolic PDE systems. The former is solved with the high-order Godunov finite volume method that ensures the pressure–velocity–temperature (PVT) equilibrium conduction. The parabolic PDEs are solved with both the implicit and the explicit locally iterative method (LIM) based on Chebyshev parameters. Numerical results are presented for several multicomponent flow problems with diffusion processes. Furthermore, we apply the proposed model to simulate the target ablation problem that is of significance to inertial confinement fusion. Comparisons with one-temperature models in literature demonstrate the ability to maintain the PVT property and superior convergence performance of the proposed model in solving multicomponent problems with diffusions. • A temperature non-equilibrium model for N -component flows with diffusion • Three equivalent formulations providing new perspectives and numerical conveniences • Models consistent with thermodynamic laws and free of nonphysical oscillations • Explicit locally iterative method for solving the nonlinear diffusion equations • Application for simulating inertial confinement fusion problems [ABSTRACT FROM AUTHOR]

Many coastal and ocean engineering flows, such as tsunamis inundating urban areas, tend to be violent. The characteristics of these damaging flow fields are three-dimensional, highly non-linear and non-hydrostatic. A fully three-dimensional free-surface fluid model is required to simulate such a flow field. Fluid simulations in the field of coastal engineering are often large-scale since large areas are the subject of the simulations. The numerical model must be not only accurate but also efficient. In recent years, the lattice Boltzmann method (LBM) has attracted much attention as a novel simulation method and has been successfully applied to various engineering fields. The LBM calculates complex phenomena in a simple framework. The density field determines the pressure field with the equation of state. This means that the LBM does not have to solve the pressure Poisson equation. However, the existing gas–liquid multi-phase flow models that employ the LBM have a critical problem. Pressure calculations with large density ratios easily become unstable, and the application of these models to violent flow fields is limited. The single-phase free-surface fluid model provides good approximations for flow problems in which the gas dynamics can be neglected. Moreover, the cumulant LBM has attracted attention because it has excellent numerical stability even for high Reynolds number flows. The single-phase free-surface flow model using the cumulant LBM is a suitable approach for simulating violent flow fields in coastal engineering. In this study, we propose a single-phase free-surface flow model based on the cumulant LBM using the volume-of-fluid (VOF) model to capture the interface. We demonstrate that the cumulant LBM is stable under violent flows and reproduces the density field well compared with the traditional single relaxation time model. We find that a larger bulk viscosity can reduce the numerical oscillation of the impact pressure acting on a structure, although a bulk viscosity that is too large reduces the accuracy and stability. The results of the proposed model are in good agreement with previous experimental results. • A VOF based single-phase free-surface flow model by the cumulant LBM is proposed. • A comparative study of the cumulant LBM and the BGK-LBM is performed. • The excellent reproducibility of the density field by the cumulant LBM is demonstrated. • The bulk viscosity has a significant influence on impact pressure is verified. [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]

• The PVMLS method can predict the pressure jump and near-to-zero spurious currents in a stationary drop problem (as a benchmark). • By deviation from unit viscosity ratio, where the discontinuities of the velocity field are not ignorable, the PMLS method cannot provide reasonable predictions of the velocity and pressure values. However, the PVMLS provides us acceptable results. • The PVMLS method provides us a better mass conservative solution when using the level set method. This is attributed to the more accurate assessment of the velocity components in the vicinity of the interface. We suggest a strategy to consider discontinuities in the two-phase flow calculations. Our approach comprises enhancing the shape functions of the finite element method (FEM) with the moving least-squares (MLS) interpolation functions. The new shape functions correlate a parameter at any arbitrary point to its surrounding nodes instead of an element's nodes. We name this strategy the "moving least-squares" aided "finite element method" (MLS-FEM). In a previous paper Mostafaiyan et al., we have employed the concept of the MLS-FEM to develop the PMLS (pressure shape function enhanced by the MLS interpolation functions) method, which predicts pressure discontinuities due to the surface tension forces. We take another additional step to consider velocity and pressure discontinuities in a domain with two different fluids. Therefore, we use the MLS technique to enhance the pressure (P) and velocity (V) shape functions. We name this scheme PVMLS (pressure and velocity shape functions enhanced by the MLS technique). We validate the PVMLS method with a stationary drop problem (as a benchmark). We show that the previous PMLS method fails to predict an accurate pressure or smooth streamlines by increasing the Capillary number and deviating from the unit viscosity ratio. However, the PVMLS method provides more accurate results since it considers velocity as a discontinuous parameter. Also, we compare the results of the PVMLS method at very high viscosity ratios (undeformable fluid) with a boundary-fitted single-phase problem. The reported similarities between the predicted pressure values and streamlines in both strategies demonstrate the reliability of the PVMLS method. Finally, we discuss that by employing the PVMLS method to calculate the velocity field, the interface advection will be more mass-conservative. [ABSTRACT FROM AUTHOR]

Abstract: Reynolds’ lubrication theory has been widely used to study thin-region fluid flows for a variety of scientific and manufacturing applications. In this work, we set forth an extension of this theory to model the effect of free fluid interfaces and fluid–structural interactions in lubrication films. This model is implemented using curvilinear shell elements in a general three-dimensional finite element code, allowing the study of lubrication flows in arbitrarily complex geometries. This implementation also allows coupling with continuum mechanics, such as solid body deformation, through lubrication-based and fluid–structural interactions. Simulations using this model are compared to analytical solutions and experimental results for a number of model problems. [Copyright &y& Elsevier]

Abstract: Methodology for performing large scale parallel numerical simulations of two-phase flow is presented that uses a three-dimensional (3-D) finite element method (FEM) solver, PHASTA, to perform the simulation and a parallel mesh adaptation code, phParAdapt, to iteratively refine and coarsen regions of the solution domain. This version of PHASTA uses a stabilized FEM to discretize the 3-D Incompressible Navier–Stokes (INS) equations plus a level set method to capture the two-phase interface. The phParAdapt code takes the current parallel mesh along with the PHASTA flow solution and, using various user-specified correction indicators as input, performs a parallel mesh refinement/coarsening procedure. Utilizing local mesh modification operators, element sizes are adjusted to equally distribute the errors across the distributed mesh during the mesh refinement/coarsening procedure. Numerical simulations ranging from simple canonical test problems up to an experimental annular steam/water flow condition were performed to illustrate this methodology. The annular flow simulation captured the instabilities that generate both the ripple and roll wave like structures on the steam/water interface and the droplet entrainment mechanisms expected in annular two-phase flows. [Copyright &y& Elsevier]

Abstract: Underwater explosions present many challenges for numerical modeling. The density ratio between explosion gases and the surrounding liquid are typically , and the pressure ratios can be just as high. We develop a cell-centered finite volume method to solve the governing equations of a two-phase homogeneous fluid. Isentropic and isothermal equations of state are used to relate densities and pressure, in lieu of solving an energy equation. A volume fraction is used to distinguish between the disparate phases. A pressure-based, segregated algebraic solution procedure is used to solve for the primitive variables representing volume fraction, velocity, and piezometric pressure. Numerical examples include verification and validation for a number of canonical test cases. In particular, we examine an advecting material interface and show the absence of pressure oscillations across the contact discontinuity. The non-conservative form of our equations does not guarantee exact mass balance, but numerical experiments indicate that this dissipative mechanism has a stabilizing affect on the method. Shock tube and axisymmetric underwater explosion problems are presented to demonstrate the robustness of the algorithm when very large density and pressure discontinuities are present. We simulate a shallow water explosion in three dimensions and examine the effects on the free surface and explosion bubble topology. [Copyright &y& Elsevier]

Abstract: A suspension balance model (SBM) is implemented to describe the shear-driven migration of particles in noncolloidal suspensions in the context of a finite element (FE) solver. Before developing the FE methodology, the SBM is analyzed in the context of a rigorous two-phase averaging procedure, in which the traditional SBM model can be thought of as an approximate closure relationship for the rigorous two-phase equations. It is shown that the standard SBM equations are inconsistent, which is demonstrated analytically for the case of Couette flow. A FE model is developed using a corrected set of SBM equations, and the numerical techniques needed to handle the anisotropic Q-tensor and FE stabilization are detailed. The resultant FE-SBM method is tested using a Couette geometry and compared with existing models and experiments. A high level of sensitivity of the particle migration to the chosen viscosity model is noted, as well as the influence of excess diffusion caused by the FE stabilization procedure. The FE-SBM method is also used in conjunction with an arbitrary Lagrangian–Eulerian formulation to simulate the deflection of the free surface in a Couette cell. Secondary flows are observed in the free-surface simulation results, and the underlying mechanisms driving these secondary flows are explored. [Copyright &y& Elsevier]

Abstract: Uncertainty quantification (UQ) deals with providing reasonable estimates of the uncertainties associated with an engineering model and propagating them to final engineering quantities of interest. We present a conceptual UQ framework for the case of shock hydrodynamics with Euler’s equations where the uncertainties are assumed to lie principally in the equation of state (EOS). In this paper we consider experimental data as providing both data and an estimate of data uncertainty. We propose a specific Bayesian inference approach for characterizing EOS uncertainty in thermodynamic phase space. We show how this approach provides a natural and efficient methodology for transferring data uncertainty to engineering outputs through an EOS representation that understands and deals consistently with parameter correlations as sensed in the data. Historically, complex multiphase EOSs have been built utilizing tables as the delivery mechanism in order to amortize the cost of creation of the tables over many subsequent continuum scale runs. Once UQ enters into the picture, however, the proper operational paradigm for multiphase tables become much less clear. Using a simple single-phase Mie–Grüneisen model we experiment with several approaches and demonstrate how uncertainty can be represented. We also show how the quality of the tabular representation is of key importance. As a first step, we demonstrate a particular tabular approach for the Mie–Grüneisen model which when extended to multiphase tables should have value for designing a UQ-enabled shock hydrodynamic modeling approach that is not only theoretically sound but also robust, useful, and acceptable to the modeling community. We also propose an approach to separate data uncertainty from modeling error in the EOS. [Copyright &y& Elsevier]

Abstract: A Runge–Kutta discontinuous Galerkin method is developed for the modeling of reactive compressible multiphase flows. From the work developed in [1], where a discontinuous Galerkin formulation was obtained for inert flows based on the ideas of [2,3], we introduce a reactive Riemann problem [4] so as to take into account the reactions we are interested in (i.e. reactions with infinitely fast time rates). Several reactive examples are presented. The corresponding results show the high capabilities of the method, which can simulate the strong density and pressure ratios, and also has no problem whenever a phase appears or disappears. [Copyright &y& Elsevier]

Abstract: In this paper, we present a Highly Parallel Particle-laden flow Solver for Turbulence Research (HiPPSTR). HiPPSTR is designed to perform three-dimensional direct numerical simulations of homogeneous turbulent flows using a pseudospectral algorithm with Lagrangian tracking of inertial point and/or fluid particles with one-way coupling on massively parallel architectures, and is the most general and efficient multiphase flow solver of its kind. We discuss the governing equations, parallelization strategies, time integration techniques, and interpolation methods used by HiPPSTR. By quantifying the errors in the numerical solution, we obtain optimal parameters for a given domain size and Reynolds number, and thereby achieve good parallel scaling on processors. [Copyright &y& Elsevier]

Abstract: We present an exact as well as two new approximate Riemann solvers for phase boundaries in compressible multiphase flow without mass transfer governed by the Euler equations. These Riemann solvers are designed for the simulation of compressible tow-phase flow in the framework of a sharp interface approach. The focus lies thereby on the accuracy as well as on the computational efficiency of the Riemann solvers. Furthermore, the approximate Riemann solvers are suitable for general equations of state, which do not have to be given in a closed analytical form and can include surface tension effects at the phase boundaries. Numerical tests in the form of two-phase shock-tube problems and droplet-shock interactions conclude the presentation. [Copyright &y& Elsevier]

Abstract: Eight equations of state (EOS) have been evaluated for the simulation of compressible liquid water properties, based on empirical correlations, the principle of corresponding states and thermodynamic relations. The IAPWS-IF97 EOS for water was employed as the reference case. These EOSs were coupled to a modified AUSM+-up convective flux solver to determine flow profiles for three test cases of differing flow conditions. The impact of the non-viscous interaction term discretisation scheme, interfacial pressure method and selection of low-Mach number diffusion were also compared. It was shown that a consistent discretisation scheme using the AUSM+-up solver for both the convective flux and the non-viscous interfacial term demonstrated both robustness and accuracy whilst facilitating a computationally cheaper solution than discretisation of the interfacial term independently by a central scheme. The simple empirical correlations gave excellent results in comparison to the reference IAPWS-IF97 EOS and were recommended for developmental work involving water as a cheaper and more accurate EOS than the more commonly used stiffened-gas model. The correlations based on the principles of corresponding-states and the modified Peng–Robinson cubic EOS also demonstrated a high degree of accuracy, which is promising for future work with generic fluids. Further work will encompass extension of the solver to multiple dimensions and to account for other source terms such as surface tension, along with the incorporation of phase changes. [Copyright &y& Elsevier]

Abstract: Insight into the spatiotemporal evolution of particle size distribution (PSD) is very useful in many natural and engineering systems in which the multiphase fields are spatially inhomogeneous and complicated dynamic processes of particle population, e.g., coagulation between particles, occur with field-dependent rates. Traditional population balance modeling (PBM) is usually used to simulate spatially homogeneous dynamic processes, only obtaining the time evolution of PSD. In this paper, we presented an algorithm to predict the spatiotemporal evolution of PSD accounting for mutual coupling of particle population and hydrodynamics. The differentially-weighted Monte Carlo method for PBM is used to simulate coagulation behavior of particles in each grid that is considered to be spatially homogeneous, and the transport behavior of fluid and particles towards neighbor grids that are spatially inhomogeneous are described by general conservation equations of multiphase flows. The simulation strategy is based on the selection of a time step within which the fluid transport, the particle transport and the particle dynamics are uncoupled and then separately simulated. A limiting case of the coarse high-inertia particles whose motion is independent of surrounding fluid is chosen to validate the population balance-Monte Carlo (PBMC) method for the spatiotemporal evolution of PSD. The computational time is found to be less by a factor of 10 compared to the direct numerical simulation (DNS), yielding reasonably closer predictions of spatiotemporal particle size distributions. [Copyright &y& Elsevier]

Abstract: We present a topology optimization method to systematically design the layout and shape of flow channels in micro-mixers for miscible fluids under steady-state conditions. The multi component flow is predicted by a multi-relaxation time lattice Boltzmann method (MRT-LBM) which allows independent control of Reynolds and Schmidt numbers. The MRT-LBM is verified against results of a passive scalar finite element advection–diffusion model. The geometry of the flow channels is described by a material distribution approach by varying the porosity of a fictitious material. While this material model penalizes fluid velocity it does not prevent diffusion through porous material. We show that for Péclet numbers greater than 1 the diffusion of fluids through porous material does not significantly affect mixing predictions. The material distribution is optimized by a gradient-based optimization scheme using adjoint sensitivities to compute the derivatives of the objective and constraints. For a two-dimensional model problem, we compare optimization results for various formulations of the design problem. The numerical results illustrate the suitability of the proposed method to optimize micro-mixers and show interesting interdependencies between the porosity model and the formulation of the objective function. [Copyright &y& Elsevier]