A high order semi-implicit IMEX WENO scheme for the all-Mach isentropic Euler system

Abstract In this paper, new high order schemes are constructed and analyzed, for the numerical solution of Euler equations of isentropic gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions for low Mach flows. High order accuracy in space is obtained by finite difference WENO schemes; while high order in time is obtained by IMEX methods with semi-implicit linearization treatment. The schemes are proven to be asymptotic preserving and asymptotic accurate as the Mach number vanishes. Several tests in one and two space dimensions illustrate the effectiveness of the proposed schemes.

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