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

The modern vision of a flow solver necessarily includes adaptivity. In particular, mesh adaptivity enables the solution strategy to allocate the resources efficiently, in that cells are concentrated in areas where they are needed, as opposed to uniform mesh refinement. 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 discretizations 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. We extend here this strategy to systems of equations, in particular to the equations governing inviscid compressible flows. While the accuracy of the reference scheme on uniform grid is preserved, storage requirements, and concurrently computational time, are heavily reduced.