This note introduces a simple metric for benchmarking shock-capturing schemes, and this metric is especially focusing on the shock-capturing overshoots, which may damage the robustness of numerical simulations, as well as the reliability of numerical results. The idea is to numerically solve the linear advection equation with square waves of different wavenumbers as initial solutions. Therefore, the exact overshoots after one step of temporal evolution can be easily calculated, and shown as a function of CFL number and reduced wavenumber. The present metric is able to quantify the numerical overshoots of shock-capturing schemes, and some new features of several canonical schemes are shown.

翻译：本说明引入了一种简单的衡量标准,用于设定冲击冲击摄取计划的基准,而这一衡量标准特别侧重于冲击捕捉过度,这可能会损害数字模拟的稳健性以及数字结果的可靠性。其想法是以数字方式解决线性平方程,以不同波数的平方波作为初始解决方案。因此,可以很容易地计算出一个时间进化步骤之后的精确多射,并显示为CFL数和减少的波数的函数。目前的衡量标准能够量化冲击捕捉计划的数字超射,并展示了几个罐头计划的一些新特征。