Manufactured Solutions for the Favre-Averaged Navier-Stokes Equations with Eddy-Viscosity Turbulence Models

Abstract

The Method of Manufactured Solutions is applied to verify the implementation of eddy viscosity turbulence models for closure of the Favre-averaged Navier-Stokes equations. In the Method of Manufactured Solutions, the governing equations are modied by the addition of source terms such that the exact solution|i.e., the manufactured solution|is known a priori. Given the exact solution, order of accuracy studies are conducted to verify that the discrete solution converges to the exact solution at the expected rate. The goal of this work is to verify the implementation of turbulence models in the Fully-Implicit NavierStokes ow solver. The turbulence model of interest for this work is the Spalart-Allmaras one-equation model, and two manufactured solutions have been examined. The rst solution is based on trigonometric functions, as commonly used in manufactured solution literature. This solution is appropriate for use in unbounded ows, enabling verication of the implementation of the free shear ow form of the model. The second solution has been newly developed in this work and is intended for use in wall-bounded ows. While other manufactured solutions for the Spalart-Allmaras model for wall-bounded ow have appeared in the literature, these solutions are shown to have features that make them illsuited to verication. To avoid such features, the wall-bounded solution developed here is loosely based on the behavior of the model solution in the inner portion of a zero-pressure boundary layer. Results obtained using both solutions show that the Fully-Implicit NavierStokes ow solver is achieving the expected second-order accuracy.