Adaptive High-Order Discretization of the Reynolds-Averaged Navier-Stokes(RANS) Equations

Abstract

The use of high-order methods to compute turbulent flows governed by the Reynolds- averaged Navier-Stokes (RANS) equations is an active research topic in the compu- tational fluid dynamics (CFD) community. However, it is well known that high-order methods for the non-smooth turbulence modeling equations are difficult to converge to the steady-state because of the numerical stiffness. The objective of this work is to de- velop a robust and efficient high-order discretization that can simulate turbulent flows governed by the Reynolds-Averaged Navier-Stokes equations, which involves the de- velopment of high-order space discretization of robust turbulence modeling equations, the improvement of time integration strategy, and the application of effective mesh adaptation methods. In the present study, correction procedure via reconstruction (CPR) high-order dis- cretization is developed to solve the Reynolds-averaged Navier-Stokes (RANS) equa- tions with the modified Spalart and Allmaras (SA) model. In this model, the non- dimensional length scale depends on the distance to the nearest wall. To compute the distance of each solution point in the domain to the nearest curved polynomial wall boundaries, the CPR high-order discretization is extended to solve the Eikonal equa- tion. On the other hand, to improve time integration strategy for the simulation of turbulent flows, the present work carried out a comparative study of several implicit time integration schemes to determine which is the most efficient, robust and general scheme. Additionally, an adjoint-based adaptive mesh refinement method is utilized to minimize the output error. Numerical results show that, to achieve a certain level of accuracy, the adaptive CPR discretization of the RANS equations with the SA model saves orders of magnitude in terms of number of degrees of freedom comparing to the numerical results of uniform mesh refinement, when applied to the simulations of turbulent flows.