In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum entropy principle, the resulting approach can robustly resolve strong discontinuities with sub-element resolution, does not require problem-dependent parameter tuning, and can be easily implemented on general unstructured meshes with relatively low computational cost. The efficacy of the approach is shown in numerical experiments on hyperbolic and mixed hyperbolic-parabolic conservation laws such as the Euler and Navier-Stokes equations for problems including extreme shocks, shock-vortex interactions, and complex compressible turbulent flows.

翻译：在这项工作中,我们为在不连续的光谱元件方法中捕捉休克提供了一种基于阳性保全酶基的适应性过滤法。通过调整过滤器强度以强制实施主动性和本地离散最小倍增原则,由此形成的方法可以有力地用分元素分辨率解决强烈的不连续性,不需要根据问题进行参数调整,并且很容易在一般非结构的、计算成本相对较低的杂草上实施。该方法的效力表现在对超双曲和混合双单曲保护法的数值实验中,如Euler和Navier-Stokes等方程式,涉及极端冲击、冲击-涡旋相互作用和复杂易压缩的动荡流等问题。