Three-Dimensional Discontinuous Galerkin h/p Adaptive Numerical Solutions for Compressible Flows

High order discontinuous Galerkin (DG) discretizations possess features making them suitable for computations of three dimensional complex flows with shocks. A key element that would make the DG method more attractive for such numerical simulations, is application of limiting procedures that ensure accurate capturing of discontinuities for three-dimensional complex flows in domains with nontrivial geometry discretized with unstructured meshes. Towards this end, a unified limiting procedure of DG discretizations in unstructured meshes is presented. Increased order of expansion and adaptive mesh refinement is introduced in the context of h/p–adaptivity in order to locally enhance resolution for three dimensional flow simulations that include discontinuities and complex flow features. Numerical results demonstrate that adaptive refinement increases the computational efficiency and the numerical accuracy of the DG method without compromising or sacrificing parallel performance.

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