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Large time step and asymptotic preserving numerical schemes for the gas dynamics equations with source terms. (English) Zbl 1284.35262

Summary: We propose large time step and asymptotic preserving schemes for the gas dynamics equations with external forces and friction terms. By asymptotic preserving, we mean that the numerical scheme is able to reproduce at the discrete level the parabolic-type asymptotic behavior satisfied by the continuous equations. By large time step, we mean that the scheme is stable under a CFL stability condition driven by the (slow) material waves, and not by the (fast) acoustic waves customary in Godunov-type schemes. Numerical evidence is proposed and shows a gain of several orders of magnitude in both accuracy and efficiency.

MSC:

35L50 Initial-boundary value problems for first-order hyperbolic systems
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35C20 Asymptotic expansions of solutions to PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics

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