Simulation of Turbulent Flows Using a Fully Discrete Explicit hp-nonconforming Entropy Stable Solver of Any Order on Unstructured Grids

Abstract

We report the numerical solution of two challenging turbulent flow test cases simulated with the SSDC framework, a compressible, fully discrete hp-nonconforming entropy stable solver based on the summation-by-parts discontinuous collocation Galerkin discretizations and the relaxation Runge—Kutta methods. The algorithms at the core of the solver are systematically designed with mimetic and structure-preserving techniques that transfer fundamental properties from the continuous level to the discrete one. We aim at providing numerical evidence of the robustness and maturity of these entropy stable scale-resolving methods for the new generation of adaptive unstructured computational fluid dynamics tools. The two selected turbulent flows are i) the flow past two spheres in tandem at a Reynolds number based on the sphere diameter of ReD = 3.9 × 103 and 104, and a Mach number of Ma∞ = 0.1, and ii) the NASA junction flow experiment at a Reynolds number based on the crank chord length of Reℓ = 2.4×106 and Ma∞ = 0.189.