Direct Riemann solvers for the time-dependent Euler equations |
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Authors: | E F Toro |
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Institution: | (1) Department of Mathematics and Physics, Manchester Metropolitan University, Manchester, UK |
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Abstract: | Approaches for finding direct, approximate solutions to the Riemann problem are presented. These result in three approximate
Riemann solvers. Here we discuss the time-dependent Euler equations but the ideas are applicable to other systems. The approximate
solvers are (i) assessed on local Riemann problems with exact solutions and (ii) used in conjunction with the Weighted Average
Flux (WAF) method to solve the two-dimensional Euler equations numerically. The resulting numerical technique is assessed
on a shock reflection problem. Comparison with experimental observation is carried out. |
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Keywords: | Hyperbolic systems Riemann problem Approximate Riemann solvers Godunov-type methods |
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