Towards a Validated DNS-Solver by Using the DLR FLOWer-Code with a Fourth Order Finite-Difference Method

Kurzfassung

Goal of the following study is the identification and benchmarking of a compressible block-structured Navier-Stokes solver for reliable DNS-predictions (Direct Numerical Simulations) which is capable to simulate relevant cases for aerospace applications as well as to fulfill the high demands of DNS calculations. These requirements are accuracy, low dissipation, low dispersion and furthermore good parallelization properties due to computationally expensive test-cases. For this purpose a $4^{th}$-order implicit finite-difference method is chosen to resolve turbulent structures as well as transitional modes even at a limited grid-resolution. This approach has shown good results in the hypersonic regime by simulating transition-scenarios by Mack-modes directly in supersonic boundary layers. It was originally derived for Large Eddy Simulations (LES) over recent years and has proven its quality regarding the necessary properties. As a test-bed, different standard-benchmarks for DNS-verification and spacial resolution are simulated for different grids and flow-conditions, like the Taylor-Green vortex, the compressible turbulent channel-flow at two Mach~numbers, the von~Karman vortex-street under consideration of acoustic pressure waves of the periodic-hill flow. Furthermore, direct numerical simulations (DNS) of Tollmien-Schlichting waves in attached boundary layers under different conditions will be shown in comparison with local linear stability theory (LST) over smooth- or rippled surfaces of flat plates and laminar wing-profiles. For all simulations, the implicit finite-difference scheme in cell-centered formulation has demonstrated it's capabilities as an efficient and reliable tool for fully resolved turbulence and transitional simulations in different Mach-number regimes under nearly incompressible, transsonic as well as supersonic flow-conditions.