A high order semi-implicit IMEX WENO scheme for the all-Mach isentropic Euler system
•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 limi...
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| Published in | Journal of computational physics Vol. 392; pp. 594 - 618 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Cambridge
Elsevier Inc
01.09.2019
Elsevier Science Ltd |
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| Abstract | •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. |
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| AbstractList | 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. •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. |
| Author | Boscarino, Sebastiano Xiong, Tao Russo, Giovanni Qiu, Jing-Mei |
| Author_xml | – sequence: 1 givenname: Sebastiano orcidid: 0000-0002-3447-8016 surname: Boscarino fullname: Boscarino, Sebastiano email: boscarino@dmi.unict.it organization: Department of Mathematics and Computer Science, University of Catania, Catania, 95125, Italy – sequence: 2 givenname: Jing-Mei surname: Qiu fullname: Qiu, Jing-Mei email: jingqiu@udel.edu organization: Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA – sequence: 3 givenname: Giovanni orcidid: 0000-0003-4215-1926 surname: Russo fullname: Russo, Giovanni email: russo@dmi.unict.it organization: Department of Mathematics and Computer Science, University of Catania, Catania, 95125, Italy – sequence: 4 givenname: Tao orcidid: 0000-0002-4912-6574 surname: Xiong fullname: Xiong, Tao email: txiong@xmu.edu.cn organization: School of Mathematical Sciences, Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian, 361005, PR China |
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| Snippet | •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... In this paper, new high order schemes are constructed and analyzed, for the numerical solution of Euler equations of isentropic gas dynamics. Material waves... |
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| SubjectTerms | 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 |
| Title | A high order semi-implicit IMEX WENO scheme for the all-Mach isentropic Euler system |
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