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The estimation of truncation error by τ-estimation revisited

机译：再谈用τ估计估计截断误差

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摘要

The aim of this paper was to accurately estimate the local truncation error of partial differential equations, that are numerically solved using a finite difference or finite volume approach on structured and unstructured meshes. In this work, we approximated the local truncation error using the τ-estimation procedure, which aims to compare the residuals on a sequence of grids with different spacing. First, we focused the analysis on one-dimensional scalar linear and non-linear test cases to examine the accuracy of the estimation of the truncation error for both finite difference and finite volume approaches on different grid topologies. Then, we extended the analysis to two-dimensional problems: first on linear and non-linear scalar equations and finally on the Euler equations. We demonstrated that this approach yields a highly accurate estimation of the truncation error if some conditions are fulfilled. These conditions are related to the accuracy of the restriction operators, the choice of the boundary conditions, the distortion of the grids and the magnitude of the iteration error.
机译：本文的目的是准确估计偏微分方程的局部截断误差，这些偏微分方程是使用有限差分或有限体积方法在结构化和非结构化网格上进行数值求解的。在这项工作中，我们使用τ估计程序近似了局部截断误差，该程序旨在比较具有不同间距的一系列网格上的残差。首先，我们将分析重点放在一维标量线性和非线性测试案例上，以检验不同网格拓扑上有限差分法和有限体积法截断误差估计的准确性。然后，我们将分析扩展到二维问题：首先是线性和非线性标量方程，最后是欧拉方程。我们证明，如果满足某些条件，则此方法可对截断误差产生高度准确的估计。这些条件与限制算子的精度，边界条件的选择，网格的变形以及迭代误差的大小有关。

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