The Variable Time-stepping DLN-Ensemble Algorithms for Incompressible Navier-Stokes Equations
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914889834954752 |
|---|---|
| author | Pei, Wenlong |
| author_facet | Pei, Wenlong |
| contents | In the report, we propose a family of variable time-stepping ensemble algorithms for solving multiple incompressible Navier-Stokes equations (NSE) at one pass. The one-leg, two-step methods designed by Dahlquist, Liniger, and Nevanlinna (henceforth the DLN method) are non-linearly stable and second-order accurate under arbitrary time grids. We design the family of variable time-stepping DLN-Ensemble algorithms for multiple systems of NSE and prove that its numerical solutions are stable and second-order accurate in velocity under moderate time-step restrictions. Meanwhile, the family of algorithms can be equivalently implemented by a simple refactorization process: adding time filters on the backward Euler ensemble algorithm. In practice, we raise one time adaptive mechanism (based on the local truncation error criterion) for the family of DLN-Ensemble algorithms to balance accuracy and computational costs. Several numerical tests are to support the main conclusions of the report. The constant step test confirms the second-order convergence and time efficiency. The variable step test verifies the stability of the numerical solutions and the time efficiency of the adaptive mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19101 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Variable Time-stepping DLN-Ensemble Algorithms for Incompressible Navier-Stokes Equations Pei, Wenlong Numerical Analysis In the report, we propose a family of variable time-stepping ensemble algorithms for solving multiple incompressible Navier-Stokes equations (NSE) at one pass. The one-leg, two-step methods designed by Dahlquist, Liniger, and Nevanlinna (henceforth the DLN method) are non-linearly stable and second-order accurate under arbitrary time grids. We design the family of variable time-stepping DLN-Ensemble algorithms for multiple systems of NSE and prove that its numerical solutions are stable and second-order accurate in velocity under moderate time-step restrictions. Meanwhile, the family of algorithms can be equivalently implemented by a simple refactorization process: adding time filters on the backward Euler ensemble algorithm. In practice, we raise one time adaptive mechanism (based on the local truncation error criterion) for the family of DLN-Ensemble algorithms to balance accuracy and computational costs. Several numerical tests are to support the main conclusions of the report. The constant step test confirms the second-order convergence and time efficiency. The variable step test verifies the stability of the numerical solutions and the time efficiency of the adaptive mechanism. |
| title | The Variable Time-stepping DLN-Ensemble Algorithms for Incompressible Navier-Stokes Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.19101 |