A residual-based h-adaptive reconstructed discontinuous Galerkin method for the compressible Euler equations on unstructured grids. (English) Zbl 1390.76379
Summary: 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 \(\mathrm{rDG}(p_{1}p_{2})\) 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.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 76Nxx | Compressible fluids and gas dynamics |
Keywords:
reconstructed discontinuous Galerkin method; high-order method; h-adaptive method; compressible Euler equationsSoftware:
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