Simulation of turbulent flows using a fully discrete explicit hp-nonconforming entropy stable solver of any order on unstructured grids

摘要

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 Re_D = 3.9 × 10~3 and 10~4, 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 Re_ℓ = 2.4 × 10~6 and Ma_∞ = 0.189.