Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
Multicomponent flow calculations by a consistent primitive algorithm
Journal of Computational Physics
Exact and approximate Riemann solvers for real gases
Journal of Computational Physics
Journal of Computational Physics
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
Discrete equations for physical and numerical compressible multiphase mixtures
Journal of Computational Physics
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
SIAM Journal on Scientific Computing
Modelling detonation waves in heterogeneous energetic materials
Journal of Computational Physics
Modelling evaporation fronts with reactive Riemann solvers
Journal of Computational Physics
Journal of Computational Physics
Modelling wave dynamics of compressible elastic materials
Journal of Computational Physics
Modeling phase transition for compressible two-phase flows applied to metastable liquids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
A new projection method is developed for the Euler equations to determine the thermodynamic state in computational cells. It consists in the resolution of a mechanical relaxation problem between the various sub-volumes present in a computational cell. These sub-volumes correspond to the ones traveled by the various waves that produce states with different pressures, velocities, densities and temperatures. Contrarily to Godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium. The pressure computation with this relaxation process replaces the use of the conventional equation of state (EOS). A simplified relaxation method is also derived and provides a specific EOS (named the Numerical EOS). The use of the Numerical EOS gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas EOS. It is then extended to the computation of interface problems separating fluids with different EOS (liquid-gas interface for example) with the Euler equations. The resulting method is very robust, accurate, oscillation free and conservative. For the sake of simplicity and efficiency the method is developed in a Lagrange-projection context and is validated over exact solutions. In a companion paper [F. Petitpas, E. Franquet, R. Saurel, A relaxation-projection method for compressible flows. Part II: computation of interfaces and multiphase mixtures with stiff mechanical relaxation. J. Comput. Phys. (submitted for publication)], the method is extended to the numerical approximation of a non-conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures.