Abstract. Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid plasma equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schemes.

No abstract

No abstract

Two-fluid plasma equations are derived by taking moments of Boltzmann equations. Ignoring collisions and viscous terms and assuming local thermodynamic equilibrium we get five moment equations for each species (electrons and ions), known as two-fluid plasma equations. These equations allow different temperatures and velocities for electrons and ions, unlike ideal magnetohydrodynamics equations. In this article, we present robust second order MUSCL schemes for two-fluid plasma equations based on Strang splitting of the flux and source terms. The source is treated both explicitly and implicitly. These schemes are shown to preserve positivity of the pressure and density. In the case of explicit treatment of source term, we derive explicit condition on the time step for it to be positivity preserving. The implicit treatment of the source term is shown to preserve positivity, unconditionally. Numerical experiments are presented to demonstrate the robustness and efficiency of these schemes.

No abstract

No abstract

The numerical simulation of non conservative systemis a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly fromconservation principles, so that in general, if themodel description is non ambiguous for smooth solutions, this is no longer the case for discontinuous solutions. From the numerical view point, this leads to the following situation: if a scheme is stable, its limit for mesh convergence will depend on its dissipative structure. This is well known since at least [1]. In this paper we are interested in the "dual" problem: given a system in non conservative form and consistent jump relations, how can we construct a numerical scheme that will, for mesh convergence, provide limit solutions that are the exact solution of the problem. In order to investigate this problem, we consider a multiphase flow model for which jump relations are known. Our scheme is an hybridation of Glimm scheme and Roe scheme. Abstract. The numerical simulation of non conservative system is a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly from conservation principles, so that in general, if the model description is non ambiguous for smooth solutions, this is no longer the case for discontinuous solutions. From the numerical view point, this leads to the following situation: if a scheme is stable, its limit for mesh convergence will depend on its dissipative structure. This is well known since at least [?]. In this paper we are interested in the "dual" problem: given a system in non conservative form and consistent jump relations, how can we construct a numerical scheme that will, for mesh convergence, provide limit solutions that are the exact solution of the problem. In order to investigate this problem, we consider a multiphase flow model for which jump relations are known. Our scheme is an hybridation of Glimm scheme and Roe scheme. AMS subject classifications: 65M06, 65M08, 65M12, 35L60, 35L65, 35L67Key words: Non conservative systems, numerical approximation, Glimm' scheme, Roe'scheme Nomenclature.• α i : volume fraction of phase i;• ρ i : density of phase i; ρ = ∑ i α i ρ i : average density,• τ i = 1/ρ i : specific volume of phase i; τ = 1/ρ: specific volume,ρ : mass fraction of phase i;• u: average velocity;• p: pressure, p i pressure of phase i;• s specific entropy, s i specific entropy of phase i, s = ∑ i Y i s i ;• ε i : specific internal energy of phase i;• e i : internal energy of phase i, e i = ρ i ε i ;• T i : temperature of phase i; * Corresponding author. Email addresses: remi.abgrall@inria.fr (R. Abgrall), hkumar@maths.iitd.ac.in (H. Kumar) http://www.global-sci.com/ Global Science Preprint• e = ∑ i α i e i : internal energy; E = e+ 1 2 ρu 2 : total energy• a: speed of sound, a i speed of sound of phase i.

No abstract