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MOC
2016

Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws

4 years 3 months ago
Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws
We study analytical properties of the Toro-Titarev solver for generalized Riemann problems (GRPs), which is the heart of the flux computation in ADER generalized Godunov schemes. In particular, we compare the Toro-Titarev solver with a local asymptotic expansion developed by LeFloch and Raviart. We show that for scalar problems the Toro-Titarev solver reproduces the truncated Taylor series expansion of LeFloch-Raviart exactly, whereas for nonlinear systems the Toro-Titarev solver introduces an error whose size depends on the height of the jump in the initial data. Thereby, our analysis answers open questions concerning the justification of simplifying steps in the Toro-Titarev solver. We illustrate our results by giving the full analysis for a nonlinear 2-by-2 system and numerical results for shallow water equations.
Claus R. Goetz, Armin Iske
Added 08 Apr 2016
Updated 08 Apr 2016
Type Journal
Year 2016
Where MOC
Authors Claus R. Goetz, Armin Iske
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