Premium
A multidimensional HLL‐Riemann solver for non‐linear hyperbolic systems
Author(s) -
Capdeville G.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2453
Subject(s) - riemann solver , solver , mathematics , roe solver , riemann problem , discretization , euler equations , polynomial , finite volume method , riemann hypothesis , interpolation (computer graphics) , mathematical analysis , computer science , mathematical optimization , animation , physics , computer graphics (images) , mechanics
This article presents a numerical model that enables to solve on unstructured triangular meshes and with a high order of accuracy, Riemann problems that appear when solving hyperbolic systems. For this purpose, we use a MUSCL‐like procedure in a ‘cell‐vertex’ finite‐volume framework. 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 barycenter of a triangular cell, from the 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. 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 use and adapt the monotonicity‐preserving limiter, initially devised by Barth ( AIAA Paper 90‐0013 , 1990). Numerical tests and comparisons with competing numerical methods enable to identify the salient features of the whole model. Copyright © 2010 John Wiley & Sons, Ltd.