Verification of Turbulence Models with a Manufactured Solution

This paper presents an exercise of Code Verification with two manufactured solutions valid for 2D RANS equations supplemented either with the one-equation Spalart & Allmaras or with the two-equation BSL k − ω turbulence model. When the manufactured solution is applied with the eddy viscosity frozen, second order convergence behaviour is shown. When the solution of the eddy viscosity is included, the discretization of the turbulence quantities transport equations appear to influence the accuracy of the mean flow solution. The results show that a first-order accurate solution of the turbulence quantities transport equations may lead to first-order accurate solutions for the mean flow variables, even if the discretization of the continuity and momentum equations is second-order accurate. It also turns out that flux limiters can have an unfavourable effect on the convergence of the results with refinement of the grid.