A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913386228350976 |
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| author | Cheng, Yu-Chen Klingenberg, Christian Touma, Rony |
| author_facet | Cheng, Yu-Chen Klingenberg, Christian Touma, Rony |
| contents | We develop a second-order accurate central scheme for the two-dimensional hyperbolic system of in-homogeneous conservation laws. The main idea behind the scheme is that we combine the well-balanced deviation method with the Kurganov-Tadmor (KT) scheme. The approach satisfies the well-balanced property and retains the advantages of KT scheme: Riemann-solver-free and the avoidance of oversampling on the regions between Riemann-fans. The scheme is implemented and applied to a number of numerical experiments for the Euler equations with gravitational source term and the results are non-oscillatory. Based on the same idea, we construct a semi-discrete scheme where we combine the above two methods and illustrate the maximum principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case Cheng, Yu-Chen Klingenberg, Christian Touma, Rony Numerical Analysis 65M08, 76M12, 35L65 We develop a second-order accurate central scheme for the two-dimensional hyperbolic system of in-homogeneous conservation laws. The main idea behind the scheme is that we combine the well-balanced deviation method with the Kurganov-Tadmor (KT) scheme. The approach satisfies the well-balanced property and retains the advantages of KT scheme: Riemann-solver-free and the avoidance of oversampling on the regions between Riemann-fans. The scheme is implemented and applied to a number of numerical experiments for the Euler equations with gravitational source term and the results are non-oscillatory. Based on the same idea, we construct a semi-discrete scheme where we combine the above two methods and illustrate the maximum principle. |
| title | A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case |
| topic | Numerical Analysis 65M08, 76M12, 35L65 |
| url | https://arxiv.org/abs/2406.07185 |