A Parallel Discontinuous Galerkin Method with Physical Orthogonal Basis on Curved Elements

This paper describes a parallel high-order Discontinuous Galerkin method based on orthogonal basis functions in physical space for arbitrary three-dimensional curved boundary geometry. The physical orthogonal basis are obtained by solving multi-stage linear systems which satisfy the orthogonal properties on arbitrary grids. On curved-boundary surfaces, the high-order Finite Element type of grids are used to represent real local curvature. An efficient parallel strategy is devised for the resulting solver, which based on OPENMP (Open Multi-Processing) automatic parallelization of independent elemental and face-based operations. The convergence accuracy of the method is tested for subsonic flow over a sphere. To further demonstrate the robustness of the method for complex curved geometry, external flow over a whole airplane configure is tested. The validation cases demonstrate the accuracy and robustness of the method.