Основные понятия
The truncation error on (p+1)-th order polynomials has zero average over the mesh period, which is a necessary condition for finite-volume schemes to exhibit the (p+1)-th order convergence on unstructured meshes.
Аннотация
The paper analyzes the convergence rate of finite-volume schemes for linear hyperbolic systems with constant coefficients on unstructured meshes. It focuses on schemes with polynomial reconstruction, the cell-centered multislope method, and edge-based schemes, including the flux correction method.
The key insights are:
If a finite-volume scheme is p-exact on non-uniform meshes and (p+1)-exact on uniform meshes, it may exhibit the (p+1)-th order convergence on non-uniform meshes, a phenomenon known as supra-convergence.
The authors propose a "zero mean error" condition, which states that the truncation error on (p+1)-th order polynomials should have zero average over the mesh period. This condition is necessary for supra-convergence and, under additional assumptions, sufficient for the (p+1)-th order convergence.
The authors verify the zero mean error condition heuristically and rigorously for the schemes considered. This explains the supra-convergence observed in previous studies and provides a unified framework to predict the convergence rate.
Numerical results are presented to demonstrate the accuracy of the multislope method for high-Reynolds number flows, which is attributed to the zero mean error property.
Статистика
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Цитаты
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