A data-driven high order sub-cell artificial viscosity for the discontinuous Galerkin spectral element method

Abstract

In this work, we present a novel higher-order smooth artificial viscosity method for the discontinuous Galerkin spectral element method and related high order methods. A neural network is used to detect the need for stabilization. Inspired by techniques from image edge detection, the neural network locates discontinuities inside mesh elements on a sub-cell level. Once the sub-cell positions of the shock fronts have been identified, the use of radial basis functions enables the construction of a high order smooth artificial viscosity field on quadrilateral meshes. We show the superiority of using higher order smooth artificial viscosity over piecewise linear approaches in particular on coarse meshes. The capabilities of the novel method are illustrated with typical applications.