We present a new Approximate Riemann Solver (ARS) for the gas dynamics equations in Lagrangian coordinates and with general non linear pressure laws. The design of this new ARS relies on a generalized Suliciu pressure relaxation approach. It gives by construction the exact solutions for isolated entropic shocks and we prove that it is Lipschitzcontinuous and satisfies an entropy inequality. Fin...

We describe an adaptive higher-order Godunov method for the compressible Euler equations with an arbitrary convex equation of state in a three-dimensional system of orthogonal curvilin-ear coordinates. The single grid algorithm is a fractional-step method which uses a second-order Godunov method for gas dynamics in each fractional step. The single grid algorithm is coupled to a conservative loc...

We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p; q) = pap2 + bq2 2 pq; 2 < ab: We combine our Godunov numerical fluxes with a simple GaussSeidel type iterations for solving the corresponding Hamilton-Jacobi Equations. The resulting algorithm is fast since it does not require a sorting strategy as does the fast marching method....

The approximation of shock waves by nite diierence schemes is considered. This question has been investigated by many authors, but mainly under some restrictions on discrete wave speeds. Basic works are due to Majda and Ralston (rational speed) and, more recently, to Liu and Yu (Diophantine speed). The main purpose of the present work is to obtain shock prooles of arbitrary speed for rather gen...

The method of calculating the system of gas dynamics equations coupled with the chemical reaction equation is considered. The flow parameters are updated in whole without splitting the system into a hydrodynamical part and an ODE part. The numerical algorithm is based on the Godunov’s scheme on deforming meshes with some modification to increase the scheme-order in time and space. The variation...

Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport. Methods. The algorithm is based on a previous work in which the MUSCL–Hancock scheme was used to evolve the induction equation. In this paper, we detail the extension of this scheme to the full MHD equations and discuss ...

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

This paper presents a new sub-grid flood inundation model obtained by upscaling the shallow water equations (SWE) to enhance efficiency in large-scale problems. The discretizes study domains using two nested meshes. are solved at coarse mesh second-order accurate space (i.e. piecewise linear reconstruction of variables) Godunov-type finite volume (FV) method, while fine is used incorporate high...