Jean-Marc Hérard

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The paper is devoted to the analysis of the real accuracy of different schemes when computing a simple hyperbolic model with source terms, which describes the motion of two-phase flows including source terms. The strategy of upwinding the source terms is investigated and compared with the standard fractional step method. A first scheme relies on the usual(More)
Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enableus to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. Lois de fermeture pour un modèle à deux pressions d'écoulement(More)
— A method to solve the Navier–Stokes equations for incompressible viscous flows and the convection and diffusion of a scalar is proposed in the present paper. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. A recently proposed diffusion scheme with interesting theoretical and numerical properties(More)
A naïve scheme to solve shallow-water equations ABSTRACT : A Finite-Volume scheme to solve shallow-water equations is proposed herein. This scheme makes use of velocity-celerity variables. It enables computing dam-break waves on dry bottom and generation of dry beds. ABRIDGED ENGLISH VERSION We introduce here a new Finite-Volume scheme in order to solve(More)
We construct an approximate Riemann solver for the isentropic Baer-Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions. The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds. In an original manner, the Riemann(More)
We provide herein some ways to compute flashing flows in variable cross section ducts, focusing on the Homogeneous Relaxation Model. The basic numerical method relies on a splitting technique which is consistent with the overall entropy inequality. The cross section is assumed to be continuous, and the Finite Volume approach is applied to approximate(More)
We propose here some explicit hybrid schemes which enable accurate computation of Euler equations with arbitrary (analytic or tabulated) equation of state (EOS). The method is valid for the exact Godunov scheme and some approximate Godunov schemes. To cite this article: T. Gallouët et al., C. R. Mecanique 330 (2002) 1–6.  2002 Académie des(More)
An approximate solution of the Riemann problem associated with a realisable and objective turbulent second-moment closure, which is valid for compressible flows, is examined. The main features of the continuous model are first recalled. An entropy inequality is exhibited, and the structure of waves associated with the non-conservative hyperbolic convective(More)