High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system
Abstract The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regim...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-11-01
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| Series: | Advances in Aerodynamics |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s42774-020-00052-9 |
| _version_ | 1818428770302820352 |
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| author | Yanqun Jiang Xun Chen Xu Zhang Tao Xiong Shuguang Zhou |
| author_facet | Yanqun Jiang Xun Chen Xu Zhang Tao Xiong Shuguang Zhou |
| author_sort | Yanqun Jiang |
| collection | DOAJ |
| description | Abstract The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe Courant-Friedrichs-Levy (CFL) restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretization of flux derivatives. The high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed IMEX WCNS. |
| first_indexed | 2024-12-14T15:06:54Z |
| format | Article |
| id | doaj.art-bb7e2d8198b64d5ab99b961cf0ee22b4 |
| institution | Directory Open Access Journal |
| issn | 2524-6992 |
| language | English |
| last_indexed | 2024-12-14T15:06:54Z |
| publishDate | 2020-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Aerodynamics |
| spelling | doaj.art-bb7e2d8198b64d5ab99b961cf0ee22b42022-12-21T22:56:40ZengSpringerOpenAdvances in Aerodynamics2524-69922020-11-012112410.1186/s42774-020-00052-9High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler systemYanqun Jiang0Xun Chen1Xu Zhang2Tao Xiong3Shuguang Zhou4Department of Mathematics, Southwest University of Science and TechnologyDepartment of Mathematics, Southwest University of Science and TechnologyDepartment of Mathematics, Southwest University of Science and TechnologySchool of Mathematical Sciences, Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen UniversityComputational Aerodynamics Institute, China Aerodynamics Research and Development CenterAbstract The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe Courant-Friedrichs-Levy (CFL) restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretization of flux derivatives. The high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed IMEX WCNS.https://doi.org/10.1186/s42774-020-00052-9High order schemeIMEX time discretizationWCNSAsymptotic-preserving propertyLow Mach numberIsentropic Euler equations |
| spellingShingle | Yanqun Jiang Xun Chen Xu Zhang Tao Xiong Shuguang Zhou High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system Advances in Aerodynamics High order scheme IMEX time discretization WCNS Asymptotic-preserving property Low Mach number Isentropic Euler equations |
| title | High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system |
| title_full | High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system |
| title_fullStr | High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system |
| title_full_unstemmed | High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system |
| title_short | High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system |
| title_sort | high order semi implicit weighted compact nonlinear scheme for the all mach isentropic euler system |
| topic | High order scheme IMEX time discretization WCNS Asymptotic-preserving property Low Mach number Isentropic Euler equations |
| url | https://doi.org/10.1186/s42774-020-00052-9 |
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