Development of an implicit high-order flux reconstruction solver for the Langtry-Menter Laminar-Turbulent Transition RANS model

Abstract

This work presents the development of the first high-order Flux Reconstruction (FR) solver for flows governed by the compressible Reynolds-Averaged Navier-Stokes (RANS) equations including Laminar-Turbulent Transition (LTT). The solver is fully implicit and implemented in the open-source COOLFluiD platform. Both the k−ω˜ Shear Stress Transport (SST) and the Langtry-Menter Local Correlation-Based Transition Model (LCTM) are implemented. Some modifications are made to the original k−ω SST model in order to obtain more robust and stable simulations. In particular, the natural logarithm of ω is transported and the equations are transformed accordingly. The implementation of the solver and the physics model are discussed in detail, as well as the residual Jacobian assembly algorithm and source term Jacobian treatment. In order to obtain adequate computational efficiency at higher orders, a semi-analytical Jacobian for the FR method is derived and investigated, as well as a specific Jacobian treatment to maintain stability and obtain favorable convergence characteristics. The solver is verified both in fully turbulent flow and in several transitional flow cases. The results of the verification cases are compared to references from the literature, showing a good agreement in all cases. Furthermore, it is shown that for increasingly high orders and fine meshes, the solver solutions coincide with each other, verifying grid independence. It is also shown that the FR method obtains accurate results on relatively coarse meshes, with a considerably larger first element height (y1+), i.e. up to y1+≃25, than state-of-the-art second-order finite volume solvers without wall-extended functions. Finally, the performance of the solver is briefly discussed, focusing on the scalability of the solver in terms of order of accuracy.