We develop a new accurate and robust numerical method for the Boussinesq paradigm equation (BPE). To design the method we first introduce a change of variables, for which the BPE takes the form of a nonlinear wave equation with the global pressure, and rewrite the wave equation as a system of conservation laws with a global flux. We then apply a Godunov-type central-upwind scheme together with ...

In this paper, a Godunov scheme on moving meshes, is studied for a kind of timedependent convection-dominated equations with dynamical boundary layers. The rate of convergence in pointwise norm, which is uniform to the small diffusion parameter 2, O(N−1 +τ), is proved, where N is the number of spatial unknowns and τ the mesh size of temporal meshes. This paper is a successful try on the converg...

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 sciences/Éditions scientifiques et médicales Elsevier ...

We present a higher order Godunov method for hyperbolic systems of conservation laws with stii, relaxing source terms. Our goal is to develop a Godunov method which produces higher order accurate solutions using time and space increments governed solely by the non-stii part of the system, i.e., without fully resolving the eeect of the stii source terms. We assume that the system satisses a cert...

A vertex-based finite volume method for Laplace operator on triangular grids is proposed in which Dirichlet boundary conditions are implemented weakly. The scheme satisfies a summation-by-parts (SBP) property including boundary conditions which can be used to prove energy stability of the scheme for the heat equation. A Nitsche-type penalty term is proposed which gives improved accuracy. The sc...

We propose and analyze a finite volume scheme of the Godunov type for conservation laws with source terms that preserve discrete steady states. The scheme works in the resonant regime as well as for problems with discontinuous flux. Moreover, an additional modification of the scheme is not required to resolve transients, and solutions of nonlinear algebraic equations are not involved. Our well-...

The finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, the artificial compression method of Harten, and Glimm’s method, a random choice method, are discussed. The methods are used to integrate the one-dimensional Eulerian form of the equations of gas d...

This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of the boundary conditions is needed for the problem to be well posed. The existence of the solution results from the convergence of the Godunov scheme. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant fo...

Abstract. We present a finite volume scheme for ideal compressible magnetohydrodynamic (MHD) equations on 2-D Cartesian meshes. The semi-discrete scheme is constructed to be entropy stable by using the symmetrized version of the equations as introduced by Godunov. We first construct an entropy conservative scheme for which su cient condition is given and we also derive a numerical flux satisfyi...