Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
Computing interface motion in compressible gas dynamics
Journal of Computational Physics
Computational methods in Lagrangian and Eulerian hydrocodes
Computer Methods in Applied Mechanics and Engineering
Why nonconservative schemes converge to wrong solutions: error analysis
Mathematics of Computation
Multicomponent flow calculations by a consistent primitive algorithm
Journal of Computational Physics
Two-dimensional front tracking based on high resolution wave propagation methods
Journal of Computational Physics
Journal of Computational Physics
A high-order Godunov method for multiple condensed phases
Journal of Computational Physics
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Three-Dimensional Front Tracking
SIAM Journal on Scientific Computing
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
Riemann-problem and level-set approaches for homentropic two-fluid flow computations
Journal of Computational Physics
A pressure-invariant conservative Godunov-type method for barotropic two-fluid flows
Journal of Computational Physics
Discrete equations for physical and numerical compressible multiphase mixtures
Journal of Computational Physics
Modelling detonation waves in heterogeneous energetic materials
Journal of Computational Physics
A five equation reduced model for compressible two phase flow problems
Journal of Computational Physics
The ghost fluid method for compressible gas-water simulation
Journal of Computational Physics
Modelling evaporation fronts with reactive Riemann solvers
Journal of Computational Physics
A compressible flow model with capillary effects
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Modelling wave dynamics of compressible elastic materials
Journal of Computational Physics
Solid-fluid diffuse interface model in cases of extreme deformations
Journal of Computational Physics
Solid-fluid diffuse interface model in cases of extreme deformations
Journal of Computational Physics
Modeling phase transition for compressible two-phase flows applied to metastable liquids
Journal of Computational Physics
Journal of Computational Physics
An interface capturing method for the simulation of multi-phase compressible flows
Journal of Computational Physics
A high-resolution mapped grid algorithm for compressible multiphase flow problems
Journal of Computational Physics
A high-order multi-dimensional HLL-Riemann solver for non-linear Euler equations
Journal of Computational Physics
Anti-diffusion interface sharpening technique for two-phase compressible flow simulations
Journal of Computational Physics
An Eulerian algorithm for coupled simulations of elastoplastic-solids and condensed-phase explosives
Journal of Computational Physics
A diffuse interface model with immiscibility preservation
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.50 |
Numerical approximation of the five-equation two-phase flow of Kapila et al. [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10) (2001) 3002-3024] is examined. This model has shown excellent capabilities for the numerical resolution of interfaces separating compressible fluids as well as wave propagation in compressible mixtures [A. Murrone, H. Guillard, A five equation reduced model for compressible two phase flow problems, Journal of Computational Physics 202(2) (2005) 664-698; R. Abgrall, V. Perrier, Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flows, SIAM Journal of Multiscale and Modeling and Simulation (5) (2006) 84-115; F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214-2248]. However, its numerical approximation poses some serious difficulties. Among them, the non-monotonic behavior of the sound speed causes inaccuracies in wave's transmission across interfaces. Moreover, volume fraction variation across acoustic waves results in difficulties for the Riemann problem resolution, and in particular for the derivation of approximate solvers. Volume fraction positivity in the presence of shocks or strong expansion waves is another issue resulting in lack of robustness. To circumvent these difficulties, the pressure equilibrium assumption is relaxed and a pressure non-equilibrium model is developed. It results in a single velocity, non-conservative hyperbolic model with two energy equations involving relaxation terms. It fulfills the equation of state and energy conservation on both sides of interfaces and guarantees correct transmission of shocks across them. This formulation considerably simplifies numerical resolution. Following a strategy developed previously for another flow model [R. Saurel, R. Abgrall, A multiphase Godunov method for multifluid and multiphase flows, Journal of Computational Physics 150 (1999) 425-467], the hyperbolic part is first solved without relaxation terms with a simple, fast and robust algorithm, valid for unstructured meshes. Second, stiff relaxation terms are solved with a Newton method that also guarantees positivity and robustness. The algorithm and model are compared to exact solutions of the Euler equations as well as solutions of the five-equation model under extreme flow conditions, for interface computation and cavitating flows involving dynamics appearance of interfaces. In order to deal with correct dynamic of shock waves propagating through multiphase mixtures, the artificial heat exchange method of Petitpas et al. [F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214-2248] is adapted to the present formulation.