Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations
Abstract In this paper, we present a mesh adaptation algorithm for the unsteady compressible Navier-Stokes equations under the framework of local discontinuous Galerkin methods coupled with implicit-explicit Runge-Kutta or spectral deferred correction time discretization methods. In both of the two...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-06-01
|
| Series: | Advances in Aerodynamics |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s42774-022-00110-4 |
| _version_ | 1811258231854465024 |
|---|---|
| author | Xiangyi Meng Yan Xu |
| author_facet | Xiangyi Meng Yan Xu |
| author_sort | Xiangyi Meng |
| collection | DOAJ |
| description | Abstract In this paper, we present a mesh adaptation algorithm for the unsteady compressible Navier-Stokes equations under the framework of local discontinuous Galerkin methods coupled with implicit-explicit Runge-Kutta or spectral deferred correction time discretization methods. In both of the two high order semi-implicit time integration methods, the convective flux is treated explicitly and the viscous and heat fluxes are treated implicitly. The remarkable benefits of such semi-implicit temporal discretizations are that they can not only overcome the stringent time step restriction compared with time explicit methods, but also avoid the construction of the large Jacobian matrix as is done for fully implicit methods, thus are relatively easy to implement. To save computing time as well as capture the flow structures of interest accurately, a local mesh refinement (h-adaptive) technique, in which we present detailed criteria for selecting candidate elements and complete strategies to refine and coarsen them, is also applied for the Navier-Stokes equations. Numerical experiments are provided to illustrate the high order accuracy, efficiency and capabilities of the semi-implicit schemes in combination with adaptive local discontinuous Galerkin methods for the Navier-Stokes equations. |
| first_indexed | 2024-04-12T18:10:12Z |
| format | Article |
| id | doaj.art-7a32de78be3e4ab5805e2718d4b69cde |
| institution | Directory Open Access Journal |
| issn | 2524-6992 |
| language | English |
| last_indexed | 2024-04-12T18:10:12Z |
| publishDate | 2022-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Aerodynamics |
| spelling | doaj.art-7a32de78be3e4ab5805e2718d4b69cde2022-12-22T03:21:51ZengSpringerOpenAdvances in Aerodynamics2524-69922022-06-014113110.1186/s42774-022-00110-4Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equationsXiangyi Meng0Yan Xu1School of Mathematical Sciences, University of Science and Technology of ChinaSchool of Mathematical Sciences, University of Science and Technology of ChinaAbstract In this paper, we present a mesh adaptation algorithm for the unsteady compressible Navier-Stokes equations under the framework of local discontinuous Galerkin methods coupled with implicit-explicit Runge-Kutta or spectral deferred correction time discretization methods. In both of the two high order semi-implicit time integration methods, the convective flux is treated explicitly and the viscous and heat fluxes are treated implicitly. The remarkable benefits of such semi-implicit temporal discretizations are that they can not only overcome the stringent time step restriction compared with time explicit methods, but also avoid the construction of the large Jacobian matrix as is done for fully implicit methods, thus are relatively easy to implement. To save computing time as well as capture the flow structures of interest accurately, a local mesh refinement (h-adaptive) technique, in which we present detailed criteria for selecting candidate elements and complete strategies to refine and coarsen them, is also applied for the Navier-Stokes equations. Numerical experiments are provided to illustrate the high order accuracy, efficiency and capabilities of the semi-implicit schemes in combination with adaptive local discontinuous Galerkin methods for the Navier-Stokes equations.https://doi.org/10.1186/s42774-022-00110-4Mesh adaptationLocal discontinuous Galerkin methodsImplicit-explicit Runge-Kutta methodsSpectral deferred correction methodsNavier-Stokes equations |
| spellingShingle | Xiangyi Meng Yan Xu Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations Advances in Aerodynamics Mesh adaptation Local discontinuous Galerkin methods Implicit-explicit Runge-Kutta methods Spectral deferred correction methods Navier-Stokes equations |
| title | Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations |
| title_full | Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations |
| title_fullStr | Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations |
| title_full_unstemmed | Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations |
| title_short | Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations |
| title_sort | adaptive local discontinuous galerkin methods with semi implicit time discretizations for the navier stokes equations |
| topic | Mesh adaptation Local discontinuous Galerkin methods Implicit-explicit Runge-Kutta methods Spectral deferred correction methods Navier-Stokes equations |
| url | https://doi.org/10.1186/s42774-022-00110-4 |
| work_keys_str_mv | AT xiangyimeng adaptivelocaldiscontinuousgalerkinmethodswithsemiimplicittimediscretizationsforthenavierstokesequations AT yanxu adaptivelocaldiscontinuousgalerkinmethodswithsemiimplicittimediscretizationsforthenavierstokesequations |