A multi-dimensional HLL-Riemann solver for Euler equations of gas dynamics This article presents a numerical model that enables to solve on unstructured triangular meshes and with a high-order of accuracy, a multi-dimensional Riemann problem that appears when solving hyperbolic problems. par For this purpose, we use a MUSCL-like procedure in a “cell-vertex” finite-volume framework. par In the first part of this procedure, we devise a four-state bi-dimensional HLL solver (HLL-2D). This solver is based upon the Riemann problem generated at the centre of gravity of a triangular cell, from surrounding cell-averages. A new three-wave model makes it possible to solve this problem, approximately. A first-order version of the bi-dimensional Riemann solver is then generated for discretizing the full compressible Euler equations. par In the second part of the MUSCL procedure, we develop a polynomial reconstruction that uses all the surrounding numerical data of a given point, to give at best third-order accuracy. The resulting over determined system is solved by using a least-square methodology. To enforce monotonicity conditions into the polynomial interpolation, we develop a simplified central WENO (CWENO) procedure. par Numerical tests and comparisons with competing numerical methods enable to identify the salient features of the whole model.
Keywords for this software
References in zbMATH (referenced in 1 article )
Showing result 1 of 1.