An implicit-explicit time stepping scheme for hybrid RANS/LES methods

Abstract

A line-implicit scheme using an implicit-explicit Runge-Kutta method is presented for time-accurate scale-resolving calculations of wall-bounded turbulent flows. Since structured grids with stretched cells are used to resolve the boundary layer, the fluxes are treated implicitly in wall-normal direction and explicitly parallel to the wall. In the interior of the flow field, explicit time integration is applied. Usually the explicit time step size of the interior is of the same size as the physical time step size required to resolve the turbulent flow features. Due to the line-implicit approach in the near-wall region, this time step size can be retained in the whole computational domain. Therefore, a reduction of the computational cost and memory usage compared to fully implicit schemes and a significant increase of the applicable time step size compared to fully explicit schemes can be achieved. Using the DLR-TAU code, the implicitexplicit time stepping scheme is applied to two laminar test cases. Similar results are obtained compared to calculations using implicit or explicit time integration methods and the advantage of the line-implicit approach regarding the CPU time is shown.