Conservative Solution Transfer Between Anisotropic Meshes for Adaptive Time-Accurate Hybridized Discontinuous Galerkin Methods
We present a hybridized discontinuous Galerkin (HDG) solver for general time-dependent balance laws. We focus in particular on a coupling of the solution process for unsteady problems with an anisotropic mesh refinement framework. The goal is to properly resolve all relevant unsteady features with the smallest number of mesh elements, and hence to reduce the computational cost of numerical simulations. The crucial step is then to transfer the numerical solution between two meshes since the anisotropic mesh adaptation is producing highly skewed unstructured grids that do not share the same topology as the original mesh where the solution is initially defined. For this purpose, we adopt the Galerkin projection as it preserves the conservation of physically relevant quantities and does not compromise the accuracy of a high-order method. We present numerical experiments verifying these properties of the overall method.
