In a recent work Feng, Liu and Wang (2020) [10], we imbedded characteristic compressing into an artificial neuron (AN) to propose a shock wave indicator on uniform mesh. In this work, the indicator is developed to unstructured grid. To achieve that, we retrain an AN on 1D randomly perturbed mesh, two prior information, (a) eigenvalue variable and (b) side-weighted average, is used in data pre-processing for reducing the influence of mesh size and keeping AN structure simple. The output of AN is then modified into a generalized and explicable form, which is used as the present shock wave indicator. We show that the troubled-cells detected by the present indicator include discontinuities caused by compressing of characteristic curves. The present indicator is then extended to multi-dimensional unstructured grid through constructing side-weighted average of eigenvalue on each spatial dimension. Numerical results are presented to demonstrate the performance of the present indicator combined with slope limiter and artificial viscosity, respectively, on various unstructured grids, the results show that the present indicator can detect shock and contact waves with low noise, and improves the indicating efficiency as well, the present indicator provides an attractive alternative in detecting shock waves on arbitrary grids and can be combined with various discontinuity-processing techniques.

在最近的一项工作 Feng, Liu and Wang (2020) [10] 中，我们将特征压缩嵌入到人工神经元 (AN) 中，以在均匀网格上提出冲击波指标。在这项工作中，指标被开发为非结构化网格。为了实现这一点，我们在一维随机扰动网格上重新训练 AN，两个先验信息，（a）特征值变量和（b）侧加权平均值，用于数据预处理以减少网格大小的影响并保持 AN 结构简单的。然后将 AN 的输出修改为通用且可解释的形式，用作当前的冲击波指标。我们表明，当前指标检测到的故障细胞包括由特征曲线压缩引起的不连续性。然后通过在每个空间维度上构建特征值的侧加权平均值，将当前指标扩展到多维非结构化网格。数值结果分别证明了结合斜率限制器和人工粘度的本指标在各种非结构化网格上的性能，结果表明本指标可以低噪声检测冲击波和接触波，并提高了指示效率好吧，本指标提供了一种有吸引力的替代方法，可以检测任意网格上的冲击波，并且可以与各种不连续性处理技术结合使用。