论文标题
改善过度冲击刺激振荡的量化
Improving the quantification of overshooting shock-capturing oscillations
论文作者
论文摘要
一种用于定量评估过冲振荡的方法旨在表征捕捉计划的性能。具体来说，按照我们以前的工作重点是仅有不连续性的案例，现在我们考虑了不连续性和平滑波的同时存在，每个案例都具有给定离散化的完整支持模式。线性对流方程被视为模型方程，并给出了标准化的测量，以使捕获方案产生的过冲振荡。因此，我们可以通过比较和分析所得的过冲，可以定量地揭示例如加权本质上是非振荡计划的休克鲁棒性。特别是，我们能够找出波数范围的范围，其中数值方案特别容易产生振荡过度的振荡。虽然通常预计较低的耗散量对于高阶方案，但我们提供了一个简单的测量方法，用于评估捕捉捕获的鲁棒性，由于捕捉捕捉计算的非线性，这并不是微不足道的。
An approach for quantitatively evaluating overshooting oscillations is designed to characterize the performance of shock-capturing schemes. Specifically, following our previous work focused on cases with only discontinuities, now we account for the concurrent presences of discontinuities and smooth waves, each with a complete set of supported modes on a given discretization. The linear advection equation is taken as the model equation, and a standardized measurement is given for overshooting oscillations produced by shock-capturing schemes. Thereby, we can quantitatively reveal the shock-capturing robustness of, for example, weighted essentially non-oscillatory schemes, by comparing and analyzing the resulting overshoots. In particular, we are able to find out the ranges of wavenumbers in which the numerical schemes are especially prone to produce overshooting oscillations. While lower dissipation is usually anticipated for high-order schemes, we provide a simple measurement for evaluating the shock-capturing robustness, which was not trivial due to the nonlinearity of shock-capturing computations.
