Asymptotic Analysis of IMEX-RK Methods for ES-BGK Model at Navier-Stokes level
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915719149518848 |
|---|---|
| author | Boscarino, Sebastiano Cho, Seung Yeon |
| author_facet | Boscarino, Sebastiano Cho, Seung Yeon |
| contents | Implicit-explicit Runge-Kutta (IMEX-RK) time discretization methods are very popular when solving stiff kinetic equations. In [21], an asymptotic analysis shows that a specific class of high-order IMEX-RK schemes can accurately capture the Navier-Stokes limit without needing to resolve the small scales dictated by the Knudsen number. In this work, we extend the asymptotic analysis to general IMEX-RK schemes, known in literature as Type I and Type II. We further suggest some IMEX-RK methods developed in the literature to attain uniform accuracy in the wide range of Knudsen numbers. Several numerical examples are presented to verify the validity of the obtained theoretical results and the effectiveness of the methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Analysis of IMEX-RK Methods for ES-BGK Model at Navier-Stokes level Boscarino, Sebastiano Cho, Seung Yeon Numerical Analysis 35Q20, 65L06, 65L04, 35Q30, 35Q31 Implicit-explicit Runge-Kutta (IMEX-RK) time discretization methods are very popular when solving stiff kinetic equations. In [21], an asymptotic analysis shows that a specific class of high-order IMEX-RK schemes can accurately capture the Navier-Stokes limit without needing to resolve the small scales dictated by the Knudsen number. In this work, we extend the asymptotic analysis to general IMEX-RK schemes, known in literature as Type I and Type II. We further suggest some IMEX-RK methods developed in the literature to attain uniform accuracy in the wide range of Knudsen numbers. Several numerical examples are presented to verify the validity of the obtained theoretical results and the effectiveness of the methods. |
| title | Asymptotic Analysis of IMEX-RK Methods for ES-BGK Model at Navier-Stokes level |
| topic | Numerical Analysis 35Q20, 65L06, 65L04, 35Q30, 35Q31 |
| url | https://arxiv.org/abs/2411.09504 |