This work reports on the performances of a fully-discrete hp-adaptive entropy stable discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations. The resulting code framework is denoted by SSDC, the first S for entropy, the second for stable, and DC for discontinuous collocated. The method is endowed with the summation-by-parts property, allows for arbitrary spatial and temporal order, and is implemented in an unstructured high performance solver. The considered class of fully-discrete algorithms are systematically designed with mimetic and structure preserving properties that allow the transfer of continuous proofs to the fully discrete setting. Our goal is to provide numerical evidence of the adequacy and maturity of these high-order methods as potential base schemes for the next generation of unstructured computational fluid dynamics tools. We provide a series of test cases of increased difficulty, ranging from non-smooth to turbulent flows, in order to evaluate the numerical performance of the algorithms. Results on weak and strong scaling of the distributed memory implementation demonstrate that the parallel SSDC solver can scale efficiently over 100,000 processes.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported in this paper was funded by King Abdullah University of Science and Technology. We are thankful to the Supercomputing Laboratory and the Extreme Computing Research Center at King Abdullah University of Science and Technology for their computing resources. Special thanks are extended to the McLaren F1 racing Team for providing experimental data and CAD geometries for the delta wing test case.