Assessment of several shock sensor schemes associated with C_0 infinity artificial viscosity on the discontinuous Galerking method

Abstract

In this work, we propose the evaluation and assessment of different shock capturing sensors in association with the numerical solution of scalar hyperbolic conservation laws. The precise shock location, as well as its jump size, are paramount in dimensioning the amount of viscosity to be artificially introduced on a per-element basis, smoothing the solution near the shocks and preserving its high order features, along with the Discontinuous Galerkin stability properties. Benchmarks will be based on the classical sensor by Persson and Peraire, designed to compare the higher polynomial mode with the whole solution expansion. The artificial viscosity method will be C_0 infinity from Glaubitz et al., where dissipation is a per-element compact and smooth function, preserving conservation and entropy stability.