A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows

Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for compressible fluid flow. The extension of the multiresolution-based mesh adaptation concept to high-order discontinuous Galerkin discretization can be performed using multiwavelets, which allow for higher-order vanishing moments, while maintaining local support. An implementation for scalar one-dimensional conservation laws has already been developed and tested. In the present paper we extend this strategy to systems of equations, in particular to the equations governing inviscid compressible flow.