GPU-accelerated Large Eddy Simulation of Hypersonic Flows

High-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for large eddy simulation of turbulent flows owing to their high accuracy and implicit dissipation properties. However, the application of DG methods for hypersonic flows is still challenging due to the high-computational cost and the lack of robust shock capturing algorithms. In this paper, we adreess the efficiency and robustness of Discontinuous Galerkin methods. To that end we develop a high-order implicit discontinuous Galerkin method for the numerical simulation of hypersonic flows on graphics processors (GPUs). The main ingredients in our approach include i) implicit high-order DG approximation on unstructured/adapted meshes, ii) shock capturing for hypersonic flows, iii) iterative solution methods with CUDA/MPI implementation on GPU clusters, and iv) effective matrix-free preconditioner with reduced basis approximation of the Jacobian matrix. Numerical results on several test cases are presented to validate our method.