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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Einfeldt, B. Munz, C.D. Roe, P.L., Sjogreen, B. (1991) On Godunov-Type Methods Near Low Densities. J. Comput. Physics 92, 273–295
Godunov, S.K. (1959) Mat. Sb. 47, p. 271
Roe, P.L. (1981) Approximate Riemann Solvers, Parameter Vectors and Difference Schemes. J. Comput. Physics 43, 357–372
Toro, E.F. (1989a) A Fast Riemann Solver with Constant Covolume Applied to the Random Choice Method. Int. J. Numerical Methods in Fluids, Vol. 9, pp. 1145–1164, 1989
Toro, E.F. (1989b) A Weighted Average Flux Method for Hyperbolic Conservation Laws. Proceedings of the Royal Society of London, A423, pp 401–418, 1989
Toro, E.F. (1991) A linearised Riemann solver for the time-dependent Euler equations of Gas Dynamics. Proc. Roy. Soc. London A 434, pp. 683–693, 1991
Toro, E.F. (1992) The Weighted Average Flux Method Applied to the Euler Equations. Phil. Trans. of the Royal Society of London, A 341, pp. 499–530, 1992
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Toro, E.F. Direct Riemann solvers for the time-dependent Euler equations. Shock Waves 5, 75–80 (1995). https://doi.org/10.1007/BF02425037
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DOI: https://doi.org/10.1007/BF02425037