On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System
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The goal of this article is to design a new approximate Riemann solver for the two-layer shallow water system which is fast compared to Roe schemes and accurate compared to Lax-Friedrichs, FORCE, or GFORCE schemes (see Castro et al. in Math. Comput. 79:1427–1472, 2010). This Riemann solver is based on a suitable decomposition of a Roe matrix (see Toumi in J. Comput. Phys. 102(2):360–373, 1992) by means of a parabolic viscosity matrix (see Degond et al. in C. R. Acad. Sci. Paris 1 328:479–483, 1999) that captures some information concerning the intermediate characteristic fields. The corresponding first order numerical scheme, which is called IFCP (Intermediate Field Capturing Parabola) is linearly L ∞-stable, well-balanced, and it doesn’t require an entropy-fix technique. Some numerical experiments are presented to compare the behavior of this new scheme with Roe and GFORCE methods.
KeywordsFinite volume method Path-conservative Two-layer shallow water
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