A residual-based h-adaptive reconstructed discontinuous Galerkin method for the compressible Euler equations on unstructured grids

摘要

In this paper, a residual-based h-adaptive high-order reconstructed DG (rDG) method based on the hybrid reconstruction strategy is developed for solving the compressible Euler equations on unstructured grids. The proposed method combines the advantages of high-order rDG discretization with appropriate residual-based error estimation techniques and h-adaptive refinement strategies, which exhibits its superior potential compared to the underlying DG methods. To be specific, a third-order hybrid rDG(p(1)p(2)) method has been carefully designed and evaluated on incompatible quadrilateral grids with hanging nodes in order to preserve 2-exactness property during the implementation of mesh refinement and coarsening. A residual-based error estimator is used as local error indicator during the h-adaptive procedures. A number of test cases are presented to assess the performance of the high-order h-adaptive rDG method. The hybrid reconstruction strategy combined with h-adaptive techniques presented in this work demonstrates promise for improving the level of accuracy and reducing the computational cost for numerical simulations of compressible inviscid flows. (C) 2017 Elsevier Ltd. All rights reserved.