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arXiv · 2404.04157

On the order of accuracy of finite-volume schemes on unstructured meshes

Pavel Bakhvalov·Mikhail Surnachev
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Abstract

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.

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Pavel Bakhvalov, Mikhail Surnachev. 2024-04-05. On the order of accuracy of finite-volume schemes on unstructured meshes. https://arxiv.org/abs/2404.04157

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