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      Low Mach number effect in simulation of high Mach number flow

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          Abstract

          In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenomena in simulating high Mach number flow, and the inaccurate pressure profile in simulating low Mach number flow. We introduced two simple low-Mach-number modifications for the classical Roe flux to decrease the difference between the acoustic and advection contributions of the numerical dissipation. While the first modification increases the local numerical dissipation, the second decreases it. The numerical tests on the double-Mach reflection problem show that both modifications eliminate the kinked Mach stem suffered by the original flux. These results suggest that, other than insufficient numerical dissipation near the shock front, the carbuncle phenomena is strongly relevant to the non-comparable acoustic and advection contributions of the numerical dissipation produced by Godunov schemes due to the low Mach number effect.

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          On the behaviour of upwind schemes in the low Mach number limit

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            Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number

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              On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes

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                Author and article information

                Journal
                23 April 2012
                Article
                1204.5092
                2ba38bef-08d9-4091-a85c-2c5114ed10cb

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                9 pages, 1 figure
                physics.flu-dyn

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