Conservative segregated solution method for turbulence model equations in compressible flows

Kurzfassung

A robust and accurate solution technique is required for the routine and reliable use of Reynolds-averaged Navier-Stokes (RANS) methods based on sophisticated turbulence models such as Reynolds Stress Transport Models (RSTM). A segregated solution method is preferred in view of code modularity and performance. In a density-based procedure, conservation errors can lead to stability problems if a turbulence model is solved in a segregated manner. In order to avoid these problems, a correction to the scalar convective fluxes has been derived which restores full consistency with the discretisation of the corresponding terms in the Navier-Stokes equations and achieves proper conservation of the transported scalar quantities. The method has been successfully implemented in the DLR CFD solver TRACE and validated using a standard Linear Eddy Viscosity Model (LEVM). With an appropriately chosen slope limiter, stable solutions have been obtained for RSTM computations. This enables the application of RSTMs to complex flows without the additional efforts of a fully coupled solution method.