A characteristic-featured shock wave indicator on unstructured grids based on training an artificial neuron

Abstract

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.