Improving the accuracy of the Jin-Xin relaxation scheme
Résumé
In the present work, a proposition is made in order to improve the accuracy of the Jin-Xin relaxation scheme. This scheme is composed of two steps: a first step in which scalar quantities corresponding to relaxed variables are advected, and a second step associated with a relaxation procedure that allows retrieving the original variables. Both steps introduce some numerical diffusion, but we focus here on the first one. The idea is to test the GRU projection step which has recently been proposed. This algorithm is very simple and has interesting anti-diffusive properties. It is based on a random choice and is directly inspired from Glimm’s ideas. This first-order scheme is very well-suited for the advection of scalar quantities with discontinuities and can be applied to unstructured meshes.
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