A residual-based h-adaptive reconstructed discontinuous Galerkin method for the compressible Euler equations on unstructured grids. (12th October 2017) - Yu, Shengjiao; Cheng, Jian; Yue, Huiqiang; Liu, Tiegang
Highlights: A third-order hybrid rDG(p1p2) method is carefully designed to preserve 2-exactness on incompatible grids with hanging nodes. A residual-based error estimator is used as local error indicator during the h-adaptive procedures. The h-adaptive rDG method shows promise in improving the level of accuracy and reducing the computational cost compared to the underlying DG method. Abstract: 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.