Criteria for Effective High-Order Meshes in Discontinuous Galerkin CFD

This paper aims to establish effective criteria for evaluating high-order meshes used in Discontinuous Galerkin methods focusing on their performance, accuracy, and computational efficiency. High-order steady-state simulations of the RAE 2822 airfoil are performed using the next-generation CFD solver CODA. The numerical results demonstrate that many metrics typically applied to linear meshes are no longer applicable to high-order meshes. In particular, high-order meshes accommodate larger y+ values, and the influence of the normal growth rate decreases as both the scheme and grid orders increase. Furthermore, the analysis of streamwise spacing suggests that greater spacing can be used with higher-order schemes and meshes. The solution-adaptive mesh refinement results highlight the ability of high-order meshes to achieve accurate solutions on relatively coarse grids, indicating their potential for reducing computational costs without sacrificing accuracy.