On the numerical overshoots of shock-capturing schemes,International Journal for Numerical Methods in Fluids

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On the numerical overshoots of shock-capturing schemes
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-06-09 , DOI: 10.1002/fld.5023
Huaibao Zhang ₁ , Fan Zhang ₂

Affiliation

This note introduces a simple metric for benchmarking shock-capturing schemes. This metric is especially focused on the shock-capturing overshoots, which may undermine the robustness of numerical simulations, as well as the reliability of numerical results. The idea is to numerically solve the model linear advection equation with an initial condition of a square wave characterized with different wavenumbers. After one step of temporal evolution, the exact numerical overshoot error can be easily determined and shown as a function of the CFL number and the reduced wavenumber. With the overshoot error quantified by the present metric, a number of representative shock-capturing schemes are analyzed accordingly, and several findings including the amplitude of overshoots non-monotonously varying with the CFL number, and the amplitude of overshoots significantly depending on the reduced wavenumber of the square waves (discontinuities), are newly discovered, which are not before.

中文翻译：

关于冲击捕获方案的数值超调

本说明介绍了一个简单的衡量标准，用于对冲击捕获方案进行基准测试。该指标特别关注冲击捕获超调，这可能会破坏数值模拟的稳健性以及数值结果的可靠性。其思想是用具有不同波数特征的方波的初始条件对模型线性平流方程进行数值求解。经过一步时间演变后，可以很容易地确定精确的数值超调误差，并将其显示为 CFL 数和减少的波数的函数。通过本指标量化的过冲误差，相应地分析了许多代表性的冲击捕获方案，并得出了一些发现，包括随着 CFL 数量非单调变化的过冲幅度，

更新日期：2021-06-09

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