论文标题
不连续光谱元素方法的基于阳性熵的自适应滤波
Positivity-Preserving Entropy-Based Adaptive Filtering for Discontinuous Spectral Element Methods
论文作者
论文摘要
在这项工作中，我们提出了一种基于阳性熵的自适应滤波方法，用于在不连续的光谱元素方法中进行冲击。通过适应滤波器强度以实现阳性和局部离散的最小熵原则，所得的方法可以通过分辨率分辨率来牢固地解决较强的不连续性，不需要问题依赖性参数调整，并且可以轻松地在非结构化网格上以相对较低的计算成本实现。该方法的功效在数值实验中显示了双曲线和混合双曲线 - 羟基保护法，例如Euler和Navier-Stokes方程，包括极端冲击，电击涡流相互作用以及复杂的可压缩湍流。
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.
