Abstract We present a systematic framework for the evaluation of shock sensors in high-resolution hybrid compact/WENO algorithms, with the goals of testing robustness and establishing accuracy in wavenumber space, with the intent to go beyond mere case-by-case comparison of solvers/sensors. Several sensors are considered, including classical ones, sensors based on multi-resolution wavelet analysis, and WENO-based shock sensors. The crucial issue of identification of suitable thresholds for the various shock sensors is tackled through a series of static tests and numerical simulations. Whereas any shock sensor with suitably low threshold is found to be effective in capturing shocks, not all of them perform equally well for waves. Performance degradation in numerical simulation of wave-like phenomena is here characterized by introducing an effective band-width for each sensor, which is found to be quite narrow for classical sensors, and much wider for WENO-based shock sensors. Based on this analysis, we also identify a new shock sensor which can be easily implemented in existing WENO-based codes. The new sensor doesn’t suffer from contamination from the WENO numerical error even for waves resolved with as few as three points-per-wavelength. This property translates into improved performance in wavenumber space, and greater resolving power in flow cases involving shocks and compressible turbulence, as demonstrated through a series of numerical tests. We emphasize that this sensor can be applied more broadly to any algorithm which contains similar smoothness indicators as classical WENO.

中文翻译：

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用于混合紧凑型/WENO 方案的震动传感器

摘要 我们提出了一个系统框架，用于评估高分辨率混合紧凑型/WENO 算法中的冲击传感器，目的是测试鲁棒性并在波数空间中建立准确性，旨在超越求解器的逐案比较/传感器。考虑了几种传感器，包括经典传感器、基于多分辨率小波分析的传感器和基于 WENO 的冲击传感器。通过一系列静态测试和数值模拟解决了为各种冲击传感器确定合适阈值的关键问题。虽然发现任何具有适当低阈值的震动传感器都能有效捕捉震动，但并非所有震动传感器对波浪的表现都一样好。波浪状现象的数值模拟中的性能下降的特征在于为每个传感器引入了有效带宽，发现对于经典传感器来说这是非常窄的，而对于基于 WENO 的冲击传感器则要宽得多。基于此分析，我们还确定了一种新的震动传感器，它可以在现有的基于 WENO 的代码中轻松实现。新传感器不会受到 WENO 数值误差的污染，即使对于每个波长只有三个点的波也是如此。这一特性转化为波数空间性能的提高，以及在涉及冲击和可压缩湍流的流动情况下的更大分辨率，如通过一系列数值测试所证明的。