Assessment of near-wall grid resolution for a h/p-adaptive high-order entropy stable solver

High-order entropy stable schemes have received increasing attention due to their robustness properties and ability to produce accurate solutions on complex geometries. This work aims to assess the near-wall solution capabilities of the compressible fully discrete solver SSDC, introduced in [1]. For this purpose, different configurations of under-resolved turbulent channel flows are studied for Reynolds numbers Re_ͳ = 182 and 544. The main goal is to get optimal grid parameters for different h/p configurations and show the feasibility of simulations with high-order polynomial solutions on relatively coarse meshes with higher off-wall space values. Optimal grid parameters for different polynomial solutions are tested with 2D and 3D simulations of flow over a NACA0012 airfoil for a Reynolds number Re = 5 × 10⁴ at an angle of attack AoA = 5°. In all the cases studied in this work, particular emphasis is placed on the computational benefits of increasing the polynomial solution p while reducing the mesh resolution h and the implementation of h/p-adaptive capabilities of the solver in order to get accurate solutions with a reduced computational cost.