A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929343363547136 |
|---|---|
| author | Cheng, Yu-Chen Klingenberg, Christian Touma, Rony |
| author_facet | Cheng, Yu-Chen Klingenberg, Christian Touma, Rony |
| contents | In this paper, we propose a new MUSCL scheme by combining the ideas of the Kurganov and Tadmor scheme and the so-called Deviation method which results in a well-balanced finite volume method for the hyperbolic balance laws, by evolving the difference between the exact solution and a given stationary solution. After that, we derive a semi-discrete scheme from this new scheme and it can be shown to be essentially TVD when applied to a scalar conservation law. In the end, we apply and validate the developed methods by numerical experiments and solve classical problems featuring Euler equations with gravitational source term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case Cheng, Yu-Chen Klingenberg, Christian Touma, Rony Numerical Analysis In this paper, we propose a new MUSCL scheme by combining the ideas of the Kurganov and Tadmor scheme and the so-called Deviation method which results in a well-balanced finite volume method for the hyperbolic balance laws, by evolving the difference between the exact solution and a given stationary solution. After that, we derive a semi-discrete scheme from this new scheme and it can be shown to be essentially TVD when applied to a scalar conservation law. In the end, we apply and validate the developed methods by numerical experiments and solve classical problems featuring Euler equations with gravitational source term. |
| title | A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.08549 |