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Compressible and incompressible limits for hyperbolic systems with relaxation. (English) Zbl 1058.76035

Summary: We present a general relaxation system which yields compressible and incompressible Euler and Navier-Stokes equations in the limit. Such a system can be used to set up relaxation schemes that work uniformly in the above limits. A higher-order nonoscillatory upwind spatial discretization and TVD implicit-explicit method for time integration are considered. Numerical computations are carried out for various test problems.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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