An Output-Based Adaptive Hybridized Discontinuous Galerkin Method on Deforming Domains

In this paper we present an output-based adaptive method for unsteady simulations of convection-dominated flows on deformable domains. The target discretization is the hybridized discontinuous Galerkin method (HDG), which offers potential computational savings at high order compared to the discontinuous Galerkin (DG) method. Mesh deformation is achieved through an arbitrary Lagrangian-Eulerian transformation with an analytical mapping. We present details of this transformation applied to the HDG system of equations, with focus on the auxiliary gradient equation, viscous stabilization, and output calculation. The temporal discretization for adaptive runs is DG in time, which lends itself to rigorous a posteriori error estimation using a fine-space discrete adjoint solution. We present modifications to the approximate factorization technique that enables an efficient DG-in-time solution for HDG. Space-time error estimates drive metric-based static spatial refinement on unstructured spatial meshes and slab-based temporal nodalizations. We show accuracy and cost comparisons between adaptive DG and HDG simulations of two-dimensional flows governed by the compressible Navier-Stokes equations on deforming domains.