Adaptive high-order discretization of the Reynolds-averaged Navier-Stokes equations

In this article, a dual-consistent high-order flux reconstruction (FR) or correction procedure via reconstruction (CPR) method is developed to solve the Reynolds-averaged Navier-Stokes (RANS) equations with the modified Spalart and Allmaras (SA) model. In this model, the non-dimensional length scale r depends on the distance to the nearest wall. To compute this distance to the nearest curved polynomial wall boundaries for each solution point, the FR/CPR high-order discretization is extended to solve the Eikonal equation. One internal and three external flow problems including a three-element high-lift configuration are considered to demonstrate the accuracy and efficiency of the present Eikonal solver. Additionally, an adjoint-based adaptive mesh refinement method is utilized to minimize the output error. The present method is demonstrated for several benchmark turbulent flow problems. The adaptive results are compared to other simulations or experimental data.