Approximate Solutions of Generalized Riemann Problems: the Toro-Titarev Solver and the LeFloch-Raviart Expansion
نویسندگان
چکیده
This work concerns the solution of generalized Riemann problems. To this end, we consider the ADER scheme of Titarev & Toro (2002), which relies on a generalization of the classical Godunov scheme. Another solution method is the power series expansion of LeFloch & Raviart (1988). We analyze the two resulting approximation schemes, where we show that for scalar 1d problems the Toro-Titarev solver and the LeFloch-Raviart expansion yield the same Taylor series expansions in time. The full analysis for the Burgers equation is finally provided.
منابع مشابه
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 expa...
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