Hp-adaptivity on anisotropic meshes for hybridized discontinuous Galerkin scheme
We present an efficient adaptation methodology on anisotropic meshes for the recently developed hybridized discontinuous Galerkin scheme for (nonlinear) convection-diffusion problems, including compressible Euler and Navier-Stokes equations. The methodology extends the refinement strategy of Dolejsi [8] based on interpolation error estimate to incorporate adjoint-based error estimate. For each element, we set the area using the adjoint-based error estimate, and we seek the anisotropy, of the element, which gives the least interpolation error in the Lq -norm (q ∈ [1, ∞)). For hp-adaptation, in addition to the anisotropy, the local polynomial degree is also chosen in such a way that the configuration gives the least interpolation error in the Lq -norm. Numerical results are shown for a scalar convection-diffusion case, as well as for inviscid subsonic, transonic and supersonic and viscous subsonic flow around the NACA0012 airfoil, to demonstrate the effectiveness of the adaptation methodology.
