No abstract

Using the concept of simple Riemann solvers, we present entropic and positive Godunov-type schemes preserving contact discontinuities for both Lagrangian and Eulerian systems of gas dynamics and magnetohydrodynamics (MHD). On the one hand, for the Lagrangian form, we develop positive and entropic Riemann solvers which can be considered as a natural extension of Roe's solvers in which the sound speed is relaxed. On the other hand, for the Eulerian form, we are able to construct by two ways Godunov-type schemes based on Lagrangian simple Riemann solvers. The first method establishes a relation between the jump of the intermediate states and the second one between the intermediate states themselves.

This paper deals with the modeling of the ionospheric plasma. Starting from the two-fluid Euler–Maxwell equations, we present two hierarchies of models. The MHD hierarchy deals with large plasma density situations while the dynamo hierarchy is adapted to lower density situations. Most of the models encompassed by the dynamo hierarchy are classical ones, but we shall give a unified presentation of them which brings a new insight into their interrelations. By contrast, the MHD hierarchy involves a new (at least to the authors) model, the massless-MHD model. This is a diffusion system for the density and magnetic field which could be of great practical interest. Both hierarchies terminate with the "classical" Striation model, which we shall investigate in detail.

Abstract. We study semilinear and quasilinear systems of the type KleinGordon-waves in the high-frequency limit. These systems are derived from the Euler-Maxwell system describing laser-plasma interactions. We prove the existence and the stability of high-amplitude WKB solutions for these systems.The leading terms of the solutions satisfy Zakharov-type equations. The key is the existence of transparency equalities for the Klein-Gordon-waves systems.These equalities are comparable to the transparency equalities exhibited by J.-L. Joly, G. Métivier and J. Rauch for Maxwell-Bloch systems.

No abstract

In this paper, a splitting strategy to simulate compressible two-phase flows using the five-equation model is presented. The main idea of the splitting is to separate the acoustic and transport phenomena. The acoustic step is solved in a non-conservative form using a scheme based on an approximate Riemann solver. Since the acoustic time step induced by the fast sound velocity is very restrictive, an implicit treatment of this step is performed. For the transport step driven by the slow material waves, an explicit scheme is used. Although non-conservative forms are used to derive numerical schemes for the two steps, the overall scheme resulting from this splitting operator strategy is conservative. It preserves contact discontinuities and reveals to be very robust compared to a standard unsplit scheme. Numerical simulations of compressible two-phase flows are presented on two-dimensional structured grids. The implicit-explicit strategy allows large time steps, which do not depend on the fast acoustic waves.

No abstract

No abstract