An adjoint-based grid adaptive discontinuous Galerkin method

Abstract

A grid adaptation method has been developed for discontinuous Galerkin discretizations of two-dimensional Euler equations. The element contribution to the global error in interested output variable is used as an indicator to drive mesh adaptation strategies. In the error indicator construction process, the adjoint variables are obtained by solving the adjoint equations with the GMRES algorithm. The solutions of the primal and adjoint problems in the enriched space of order p +1 are approximated by taking a small number of block-diagonal Jacobi iterations on the projected solutions of order p . In order to enforce the adjoint consistency, the numerical flux and output functions defined on the wall are constructed to depend only on the exterior states. The drag coefficient of NACA0012 airfoil with different orders of accuracy is used to evaluate the reliability of the output error estimation method. The subsonic and transonic inviscid flows around NACA 0012 airfoil, and the Mach 6 hypersonic flow over a half cylinder are simulated using the developed grid adaptation method. The computation results demonstrate that the adjoint-based adaptive method is very effective in reducing discretiztion errors of the output functions such as drag coefficient. The results for the subsonic flow of NACA 0012 shows that only 17% of degrees of freedom employed by the uniform refinement is required to achieve equivalent output accuracy by the adjoint-based adaptive approach.