Implementing a time-accurate implicit-explicit method with error estimation for compressible flow

Abstract

An implicit-explicit Runge-Kutta method is implemented in the DLR-TAU code to improve the time integration procedure when performing time-accurate simulations like Detached-Eddy Simulation of high Reynolds number turbulent flows. The idea is to avoid the use of the standard dual time stepping approach and instead use an explicit Runge-Kutta scheme in most parts of the grids where the stable time step size is in the order of the physical time scale to resolve the large eddies. In the boundary layers where the underlying RANS model allows for highly stretched grids the local time step reduces significantly. Therefore, fluxes along wall-normal lines are treated implicitly by the time integration scheme. The implicit-explicit scheme together with the error estimation approach is presented in detail.