Implicit unfactored implementation of two-equation turbulence models in compressible Navier-Stokes methods

An implicit unfactored method for the coupled solution of the compressible Navier-Stokes equations with two-equation turbulence models is presented. Both fluid-flow and turbulence transport equations are discretized by a characteristics-based scheme. The implicit unfactored method combines Newton subiterations and point-by-point Gauss-Seidel subrelaxation. Implicit-coupled and -decoupled strategies are compared for their efficiency in the solution of the Navier-Stokes equations in conjunction with low-Re two-equation turbulence models. Computations have been carried out for the flow over an axisymmetric bump using the k-ε and k-ω models. Comparisons have been obtained with experimental data and other numerical solutions. The present study reveals that the implicit unfactored implementation of the two-equation turbulence models reduces the computing time and improves the robustness of the CFD code in turbulent compressible flows.