A Flux-Correction Form of the Third-Order Edge-Based Scheme for a General Numerical Flux Function
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908895561121792 |
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| author | Nishikawa, Hiroaki |
| author_facet | Nishikawa, Hiroaki |
| contents | In this short note, we present a flux-correction form of the third-order edge-based scheme for the Euler equations that enables the direct use of a general flux function. The core idea is to replace, without loss of accuracy, the arithmetic average of the flux extrapolations by a general numerical flux evaluated at the edge midpoint, together with a correction term. We show that the proposed flux-correction form preserves third-order accuracy, provided that the general numerical flux is evaluated with the left and right states that are computed exactly for a quadratic function, which can be achieved effectively by the U-MUSCL scheme with κ = 1/2. Numerical results are presented to verify third-order accuracy with the HLLC and LDFSS flux functions on irregular tetrahedral grids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01938 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Flux-Correction Form of the Third-Order Edge-Based Scheme for a General Numerical Flux Function Nishikawa, Hiroaki Numerical Analysis Computational Physics In this short note, we present a flux-correction form of the third-order edge-based scheme for the Euler equations that enables the direct use of a general flux function. The core idea is to replace, without loss of accuracy, the arithmetic average of the flux extrapolations by a general numerical flux evaluated at the edge midpoint, together with a correction term. We show that the proposed flux-correction form preserves third-order accuracy, provided that the general numerical flux is evaluated with the left and right states that are computed exactly for a quadratic function, which can be achieved effectively by the U-MUSCL scheme with κ = 1/2. Numerical results are presented to verify third-order accuracy with the HLLC and LDFSS flux functions on irregular tetrahedral grids. |
| title | A Flux-Correction Form of the Third-Order Edge-Based Scheme for a General Numerical Flux Function |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2602.01938 |