Continuous Artificial-Viscosity Shock Capturing for Hybrid Discontinuous Galerkin on Adapted Meshes

Abstract

One technique for capturing shocks with high-order methods is through artificial viscosity. The key considerations of this approach are 1) deciding the amount of artificial viscosity to add; 2) maintaining stability and efficiency of the nonlinear solver; and 3) ensuring accuracy of the resulting solutions, particularly in the presence of strong shocks. To address consideration 1, we test a switch based on intraelement solution variation as well as one based on the difference between the solution and its low-order projection. To address consideration 2, we forego a complete linearization of the artificial-viscosity contribution to the residual in order to keep the residual Jacobian stencil compact. To address consideration 3, we introduce the viscosity in a piecewise-continuous fashion to avoid spurious entropy production. Furthermore, we use output-based error estimation and mesh optimization on the drag and the total enthalpy error, as well as with entropy variables, to minimize the output error. We test the shock capturing method coupled with mesh optimization on aerodynamic flow applications ranging from transonic to supersonic, which are discretized using the standard discontinuous Galerkin (DG) and hybridized DG methods. One of our findings is that the mesh optimization through error sampling and synthesis algorithm does not always generate the ideal mesh in the presence of strong shocks.