Gérard Gallice

Positive and Entropy Stable Godunov-type Schemes for Gas Dynamics and MHD Equations in Lagrangian or Eulerian Coordinates

SummaryUsing 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.

Solveurs simples positifs et entropiques pour les systèmes hyperboliques avec terme source

The notion of simple Riemann solver is introduced for hyperbolic systems with source term and entropic Godunov-type schemes are derived for gas dynamic system with gravity and Saint-Venant system. To cite this article: G. Gallice, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 713–716.

Justification of the Zakharov Model from Klein–Gordon-Wave Systems

Abstract We study semilinear and quasilinear systems of the type Klein–Gordon-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.

Schémas de type Godunov entropiques et positifs préservant les discontinuités de contact

Resume On decrit deux methodes de construction de schemas de type Godunov pour des lois de conservation. On en deduit des schemas entropiques et positifs pour la dynamique des gaz et la magnetohydrodynamique.

Schémas de type Godunov entropiques et positifs pour la dynamique des gaz et la magnétohydrodynamique lagrangiennes

Resume On construit des schemas de type Godunov entropiques et positifs pour la dynamique des gaz et la magnetohydrodynamique lagrangiennes. Ces schemas sont des extensions naturelles de schemas de Roe deja connus.

A robust implicitexplicit acoustic-transport splitting scheme for two-phase flows

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 implicitexplicit strategy allows large time steps, which do not depend on the fast acoustic waves.

SOME ACOUSTIC-TRANSPORT SPLITTING SCHEMES FOR TWO-PHASE COMPRESSIBLE FLOWS

In this paper, we present a splitting strategy to simulate compressible two-phase flows using the five-equation model [1]. The main idea of the splitting [2] is to separate the acoustic and transport phenomena. The acoustic step is solved as a Lagrangian step by using different schemes [3, 4, 5] based on approximate Riemann solvers. On the one hand, since the acoustic time step driven by the fast sound velocity is very restrictive, an implicit treatment of the Lagrangian step is performed. On the other hand, an explicit scheme is used for the transport step driven by the slow material waves. The global scheme resulting from this splitting operator strategy is conservative, positive, and preserves contact discontinuities. Numerical simulations of compressible diphasic flows are presented on 2d-structured grids. The implicitexplicit strategy allows large time steps, which do not depend on the fast acoustic waves. On supersonic velocity test case, a carbuncle phenomenon can occur with usual schemes for the Lagrangian part. However, we show that this carbuncle does not appear when the Lagrangian step is solved with a genuinely two-dimensional scheme based on a nine-point stencil [5].

Quasi-linear electron acceleration in a driven plasma wave

Saturation of electron plasma waves excited by a spatially localized driver and the electron acceleration in these plasma waves are studied by means of numerical simulations. The model consists of the set of Zakharov equations for the electron plasma and ion acoustic waves coupled to the quasi-linear equation for the electron distribution function. The saturation levels of both electron plasma and ion acoustic waves and the number and energy of hot electrons are studied in function of the driver wave number and amplitude and the size of the excitation region. A correlation between the onset of the strong Langmuir turbulence and the efficient electron heating is discussed.

Stabilized Finite Element Method for Compressible–Incompressible Diphasic Flows

This paper concerns the simulation of two immiscible fluids separated by a moving interface. In this goal, a global and simple numerical approach in which the gas is considered compressible and the liquid incompressible is elaborated. The numerical simulation of bubble dynamics phenomena is presented to illustrate the proposed method.

INTERACTION OF LASER BEAMS WITH A PLASMA

In this paper, we construct a model for the propagation of two laser beams in a plasma. The originality of our model lies in the fact that it is valid uniformly in terms of the angle between both beams while it is not the case for standard models. In a simplified case we show that the solution converges towards the solution of the classical ones for large angles.