Loosely coupled and coupled solution methods for the RANS equations and a one-equation turbulence model

Abstract

The compressible Reynolds Averaged Navier-Stokes (RANS) equations represent a system of hyperbolic–parabolic nonlinear equations, which is composed of two different systems of equations. On the one hand, the mean flow equations represent the essential part, on the other hand, a system of equations is required to take the effects of turbulence into account. Variables and parameters of one system of equations are required to describe the other system of equations. In this sense, mean flow and turbulence flow equations are only one, fully coupled system of equations. On the other hand, the coupling between the systems of equations is often not as pronounced, which is why these systems are often weakly or loosely coupled solved in implementations. Against the background of these different perspectives, this article examines whether it is advantageous to solve the systems of equations in a mathematically consistent coupled or in a loosely coupled manner. A comparative study considering a broad range of applications is performed to discuss and demonstrate possible benefits when solving the sets of equations in either a fully coupled or a loosely coupled manner.