On the order of accuracy of finite-volume schemes on unstructured meshes
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909162028400640 |
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| author | Bakhvalov, Pavel Surnachev, Mikhail |
| author_facet | Bakhvalov, Pavel Surnachev, Mikhail |
| contents | We consider finite-volume schemes for linear hyperbolic systems with constant coefficients on unstructured meshes. Under the stability assumption, they exhibit the convergence rate between $p$ and $p+1$ where $p$ is the order of the truncation error. Our goal is to explain this effect. The central point of our study is that the truncation error on $(p+1)$-th order polynomials has zero average over the mesh period. This condition is verified for schemes with a polynomial reconstruction, multislope finite-volume methods, 1-exact edge-based schemes, and the flux correction method. We prove that this condition is necessary and, under additional assumptions, sufficient for the $(p+1)$-th order convergence. Furthermore, we apply the multislope method to a high-Reynolds number flow and explain its accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the order of accuracy of finite-volume schemes on unstructured meshes Bakhvalov, Pavel Surnachev, Mikhail Numerical Analysis 65M08 G.1.8 We consider finite-volume schemes for linear hyperbolic systems with constant coefficients on unstructured meshes. Under the stability assumption, they exhibit the convergence rate between $p$ and $p+1$ where $p$ is the order of the truncation error. Our goal is to explain this effect. The central point of our study is that the truncation error on $(p+1)$-th order polynomials has zero average over the mesh period. This condition is verified for schemes with a polynomial reconstruction, multislope finite-volume methods, 1-exact edge-based schemes, and the flux correction method. We prove that this condition is necessary and, under additional assumptions, sufficient for the $(p+1)$-th order convergence. Furthermore, we apply the multislope method to a high-Reynolds number flow and explain its accuracy. |
| title | On the order of accuracy of finite-volume schemes on unstructured meshes |
| topic | Numerical Analysis 65M08 G.1.8 |
| url | https://arxiv.org/abs/2404.04157 |