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

• Published in: Journal of computational physics Vol. 392; pp. 594 - 618
• Main Authors: Boscarino, Sebastiano, Qiu, Jing-Mei, Russo, Giovanni, Xiong, Tao
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.09.2019; Elsevier Science Ltd
• Subjects: Acoustic waves; Asymptotic methods; Asymptotic preserving; Asymptotic properties; Computational physics; Euler-Lagrange equation; Finite difference method; Gas dynamics; IMEX; Incompressible solver; Low-Mach; Mach number; Semi-implicit; WENO reconstruction; Semi-implicit; IMEX; WENO reconstruction; Low-Mach; Incompressible solver; Asymptotic preserving
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.04.057

•A high order all-Mach number solver for isentropic Euler equations is presented.•It is based on finite difference in space and IMEX in time.•Material waves are treated explicitly, while acoustic waves are treated implicitly.•The schemes are shown to be asymptotic preserving with incompressible limit.•Several tests in one and two space dimensions show the effectiveness of the schemes. 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.