Simplified asymptotic equations for the transition to detonation in reactive granular materials
SIAM Journal on Applied Mathematics
Why nonconservative schemes converge to wrong solutions: error analysis
Mathematics of Computation
Journal of Computational Physics
Traveling-wave solutions of convection-diffusion systems in nonconservation form
SIAM Journal on Mathematical Analysis
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
A Simple Method for Compressible Multifluid Flows
SIAM Journal on Scientific Computing
A high-resolution numerical method for a two-phase model of deflagration-to-detonation transition
Journal of Computational Physics
Mathematical and numerical modeling of two-phase compressible flows with micro-inertia
Journal of Computational Physics
Modelling detonation waves in heterogeneous energetic materials
Journal of Computational Physics
Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas
Journal of Computational Physics
Modelling evaporation fronts with reactive Riemann solvers
Journal of Computational Physics
The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow
Journal of Computational Physics
Implementation of WENO schemes in compressible multicomponent flow problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Comparison and validation of multi phase closure models
Computers & Mathematics with Applications
Solid-fluid diffuse interface model in cases of extreme deformations
Journal of Computational Physics
Journal of Computational Physics
Conservative Models and Numerical Methods for Compressible Two-Phase Flow
Journal of Scientific Computing
HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow
Journal of Computational Physics
A discrete model for compressible flows in heterogeneous media
Journal of Computational Physics
A gas-kinetic BGK scheme for gas-water flow
Computers & Mathematics with Applications
Journal of Scientific Computing
Wavefronts in a Relativistic Two-Phase Turbulent Flow
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Journal of Computational Physics
An accurate low-Mach scheme for a compressible two-fluid model applied to free-surface flows
Journal of Computational Physics
Hi-index | 31.52 |
We have recently proposed, in [21], a compressible two-phase unconditionally hyperbolic model able to deal with a wide range of applications: interfaces between compressible materials, shock waves in condensed multiphase mixtures, homogeneous two-phase flows (bubbly and droplet flows) and cavitation in liquids. One of the difficulties of the model, as always in this type of physical problems, was the occurrence of non-conservative products. In [21], we have proposed a discretisation technique that was without any ambiguity only in the case of material interfaces, not in the case of shock waves. This model was extended to several space dimensions in [24], In this paper, thanks to a deeper analysis of the model, we propose a class of schemes that are able to converge to the correct solution even when shock waves interact with volume fraction discontinuities. This analysis provides a more accurate estimate of closure terms, but also an accurate resolution method for the conservative fluxes as well as non-conservative terms even for situations involving discontinuous solutions. The accuracy of the model and method is clearly demonstrated on a sequence of difficult test problems.