Navier-Stokes equations with several independent pressure laws and explicit predictor-corrector schemes |
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Authors: | C Chalons F Coquel |
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Institution: | 1. Université Paris 7 & Laboratoire JLL, U.M.R. 7598, Bo?te courrier 187, 75252, Paris Cedex 05, France 2. Centre National de la Recherche Scientifique & Laboratoire JLL, U.M.R. 7598, Bo?te courrier 187, 75252, Paris Cedex 05, France
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Abstract: | This work is concerned with the numerical capture of stiff viscous shock solutions of Navier-Stokes equations for complex
compressible materials, in the regime of large Reynolds numbers. After 2] and 6], a relevant numerical capture is known
to require the satisfaction of an extended set of non classical Rankine-Hugoniot conditions due to the non conservation form
of the governing PDE model. Here, we show how to enforce their validity at the discrete level without the need for solving
local non linear algebraic problems. Non linearities are bypassed when introducing new averaging techniques which are proved
to satisfy all the desirable stability properties when invoking suitable approximate Riemann solutions. A relaxation procedure
is proposed to that purpose with the benefit of a fairly simple overall numerical method. |
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Keywords: | 35K55 65M99 76M12 76N15 |
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