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Article

Remaki, L.
Riemann solution for hyperbolic equations with discontinuous coefficients. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 188-196
MSC: 35L40, 35L45, 35L50, 35R05, 65M08, 76P05 | MR 3204443 | Zbl 1340.35195
Keywords:
hyperbolic equations; Riemann solution; discontinuous coefficients
Summary:
This paper deals with a Riemann solution for scalar hyperbolic equations with discontinuous coefficients. In many numerical schemes of Godunov type in fluid dynamics, electromagnetic and so on, usually hyperbolic problems are solved to estimate fluxes. The exact solution is generally difficult to obtain, but good approximations are provided in many situations like Roe and HLLC Riemann solvers in fluid. However all these solvers assumes that the acoustic waves speeds are continuous which is not true as we will show in this paper. A new Riemann solver is then proposed based on previous work of the author and an application to a gas-particle model for a 90 degree curved bend is performed.
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