Approximate solutions of generalized Riemann problems [chapter]

Claus Goetz, Armin Iske
2012 Numerical Methods for Hyperbolic Equations  
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.
doi:10.1201/b14172-37 fatcat:bdqumxhy3zdzdoqxiubc75lupq