改进对激波捕捉格式中超调振荡的量化
Improving the quantification of overshooting shock-capturing oscillations
AI总结：
本研究针对间断与光滑波共存场景，提出一种基于线性平流方程的激波捕捉超调振荡标准化定量评估方法，可分析格式鲁棒性并定位易超调的波数范围，解决了非线性激波计算鲁棒性难度量的问题。
摘要：
本文设计了一种定量评估超调振荡的方法，用于表征激波捕捉格式的性能。具体而言，继我们此前仅关注含间断情形的工作之后，本研究考虑了间断与光滑波同时存在的情况，二者在给定离散格式下均具备一整套支持模态。研究以线性平流方程作为模型方程，针对激波捕捉格式产生的超调振荡给出了标准化度量方法。由此，我们可通过对比分析所得超调量，定量揭示例如加权基本无振荡（WENO）格式等的激波捕捉鲁棒性。尤为重要的是，我们能够找出数值格式尤其容易产生超调振荡的波数范围。尽管高阶格式通常期望具备更低的耗散性，我们提供了一种用于评估激波捕捉鲁棒性的简易度量方法，而由于激波捕捉计算的非线性，这一度量此前并非易事。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
