An Adjoint-Based h-Adaptive Reconstructed Discontinuous Galerkin Method for the Steady-State Compressible Euler Equations (Communications in Computational Physics, 2019)
In this paper, an adjoint-based h-adaptive high-order reconstructed DG(rDG) method is introduced for solving the two dimensional steady-state compressible Euler equations. Based on the hybrid reconstruction strategy developed in [9, 28],adjoint-based a posteriori error estimation is further derived and developed for h-adaption. The formulation of error indicator is carefully investigated in order to deliver better approximation with respect to the error in the computed output functional.In order to evaluate the performance of the proposed method, an adjoint-based h-adaptive rDG(p1 p2) method is implemented, in which a hybrid p1 p2 reconstructionand a hybrid p2 p3 reconstruction are adopted in the primal solver and the adjointsolver to obtain the primal solution and the adjoint solution, respectively. A number oftypical test cases are selected to assess the performance of the adjoint-based h-adaptivehybrid rDG method. The hybrid reconstruction strategy combined with h-adaptivetechniques based on adjoint-based error estimate presented in this work demonstratesits capacity in reducing the error with respect to the computed output functional andimproving the level of accuracy for numerical simulations of the compressible inviscidflows.