On the use of symmetrizing variables for vacuum

The paper is devoted to the computation of shallow-water equations (or Euler equations) when the flow may include dry areas. This is achieved with the help of some symmetrizing variables

Numerical modeling of two-phase flows using the two-fluid two-pressure approach

The present paper is devoted to the computation of two-phase flows using the two-fluid approach. The overall model is hyperbolic and has no conservative form. No instantaneous local equilibrium between phases is assumed, which results in a two-velocity twopressure model. Original closure laws for interfacial velocity and interfacial pressure are proposed. These closures allow to deal with discontinuous solutions such as shock waves and contact discontinuities without ambiguity for the definition of Rankine-Hugoniot jump relations. Each field of the convective system is investigated, providing that the maximum principle for the volume fraction and the positivity of densities and internal energies are ensured when focusing on the Riemann problem. Two Finite Volume methods are presented, based on the Rusanov scheme and on an approximate Godunov scheme. Relaxation terms are taken into account using a fractional step method. Eventually, numerical tests illustrate the ability of both methods to compute two-phase flows

Numerical modeling of two-phase flows using the two-fluid two-pressure approach

The present paper is devoted to the computation of two-phase flows using the two-fluid approach. The overall model is hyperbolic and has no conservative form. No instantaneous local equilibrium between phases is assumed, which results in a two-velocity twopressure model. Original closure laws for interfacial velocity and interfacial pressure are proposed. These closures allow to deal with discontinuous solutions such as shock waves and contact discontinuities without ambiguity for the definition of Rankine-Hugoniot jump relations. Each field of the convective system is investigated, providing that the maximum principle for the volume fraction and the positivity of densities and internal energies are ensured when focusing on the Riemann problem. Two Finite Volume methods are presented, based on the Rusanov scheme and on an approximate Godunov scheme. Relaxation terms are taken into account using a fractional step method. Eventually, numerical tests illustrate the ability of both methods to compute two-phase flows

Some recent Finite Volume schemes to compute Euler equations using real gas EOS

International audienceThis paper deals with the resolution by Finite Volume methods of Eu-ler equations in one space dimension, with real gas state laws (namely perfect gas EOS, Tammann EOS and Van Der Waals EOS). All tests are of unsteady shock tube type, in order to examine a wide class of solutions, involving Sod shock tube, stationary shock wave, simple contact disconti-nuity, occurence of vacuum by double rarefaction wave, propagation of a 1-rarefaction wave over \vacuum", ... Most of methods computed herein are approximate Godunov solvers : VFRoe, VFFC, VFRoe ncv (; u; p) and PVRS. The energy relaxation method with VFRoe ncv (; u; p) and Rusanov scheme have been investigated too. Qualitative results are presented or commented for all test cases and numerical rates of convergence on some test cases have been measured for rst and second order (Runge-Kutta 2 with MUSCL reconstruction) approximations. Note that rates are measured on solutions involving discontinuities, in order to estimate the loss of accuracy due to these discontinuities

On the use of symmetrizing variables for vacuum

The paper is devoted to the computation of shallow-water equations (or Euler equations) when the flow may include dry areas. This is achieved with the help of some symmetrizing variables

On the use of symmetrizing variables for vacuum

The paper is devoted to the computation of shallow-water equations (or Euler equations) when the flow may include dry areas. This is achieved with the help of some symmetrizing variables