Convection Treatment for RANS Turbulence Model Equations

Abstract

In the context of finite-volume methods it is generally accepted that at least second order discretization schemes should be considered for the mean flow equations due to their superior accuracy compared to first order schemes. For turbulence model equations, the situation is not so clear when the Boussinesq approximation is applied. Since the coupling of the turbulence model into the mean flow equations is rather weak (via the eddy viscosity and a rather small contribution to the turbulent kinetic energy to the total energy conservation), one can hope for a minor effect on solution accuracy. The goal of this article is to identify the relevant details required in a careful implementation of a first order treatment of the convective part of the turbulence model, such that the obtained results remain comparable to a fully second order discretization. Compelling arguments are given that a first order treatment of turbulence does not necessarily lead to a relevant loss of accuracy in the investigated cases, while yielding a significant gain in robustness.