Numerical Analysis of Locally Adaptive Penalty Methods For The Navier-Stokes Equations
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909173659205632 |
|---|---|
| author | Fang, Rui |
| author_facet | Fang, Rui |
| contents | Penalty methods relax the incompressibility condition and uncouple velocity and pressure. Experience with them indicates that the velocity error is sensitive to the choice of penalty parameter $ε$. So far, there is no effective á prior formula for $ε$. Recently, Xie developed an adaptive penalty scheme for the Stokes problem that picks the penalty parameter $ε$ self-adaptively element by element small where $\nabla \cdot u^h$ is large. Her numerical tests gave accurate fluid predictions. The next natural step, developed here, is to extend the algorithm with supporting analysis to the non-linear, time-dependent incompressible Navier-Stokes equations. In this report, we prove its unconditional stability, control of $\|\nabla \cdot u^h\|$, and provide error estimates. We confirm the predicted convergence rates with numerical tests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Analysis of Locally Adaptive Penalty Methods For The Navier-Stokes Equations Fang, Rui Numerical Analysis Penalty methods relax the incompressibility condition and uncouple velocity and pressure. Experience with them indicates that the velocity error is sensitive to the choice of penalty parameter $ε$. So far, there is no effective á prior formula for $ε$. Recently, Xie developed an adaptive penalty scheme for the Stokes problem that picks the penalty parameter $ε$ self-adaptively element by element small where $\nabla \cdot u^h$ is large. Her numerical tests gave accurate fluid predictions. The next natural step, developed here, is to extend the algorithm with supporting analysis to the non-linear, time-dependent incompressible Navier-Stokes equations. In this report, we prove its unconditional stability, control of $\|\nabla \cdot u^h\|$, and provide error estimates. We confirm the predicted convergence rates with numerical tests. |
| title | Numerical Analysis of Locally Adaptive Penalty Methods For The Navier-Stokes Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.11712 |