A Comparison of Hybridized and Standard DG Methods for Target-Based hp-Adaptive Simulation of Compressible Flow

摘要

We present a comparison between hybridized and non-hybridized discontinuousGalerkin methods in the context of target-based hp-adaptation for compressibleflow problems. The aim is to provide a critical assessment of the computationalefficiency of hybridized DG methods. Hybridization of finite elementdiscretizations has the main advantage, that the resulting set of algebraicequations has globally coupled degrees of freedom only on the skeleton of thecomputational mesh. Consequently, solving for these degrees of freedom involvesthe solution of a potentially much smaller system. This not only reducesstorage requirements, but also allows for a faster solution with iterativesolvers. Using a discrete-adjoint approach, sensitivities with respect tooutput functionals are computed to drive the adaptation. From the errordistribution given by the adjoint-based error estimator, h- or p-refinement ischosen based on the smoothness of the solution which can be quantified byproperly-chosen smoothness indicators. Numerical results are shown forsubsonic, transonic, and supersonic flow around the NACA0012 airfoil.hp-adaptation proves to be superior to pure h-adaptation if discontinuous orsingular flow features are involved. In all cases, a higher polynomial degreeturns out to be beneficial. We show that for polynomial degree of approximationp=2 and higher, and for a broad range of test cases, HDG performs better thanDG in terms of runtime and memory requirements.