High-Order LES Simulations using Implicit-Explicit Runge-Kutta Schemes

For many flow problems modeled by Large Eddy Simulation (LES), the computational meshes are such that a majority of the elements would allow for explicit timestepping, but the CFL-condition is limited by the smaller stretched elements in the boundary layers. We propose an implicit-explicit time-integration scheme that uses an implicit solver only for the smaller portion of the domain where it is required to avoid severe timestep restrictions, but an efficient explicit solver for the rest of the domain. We use the Runge-Kutta IMEX schemes and consider several schemes of varying number of stages, orders of accuracy, and stability properties, and study the stability and the accuracy of the solver. We also show the application of the technique to a realistic LES-type problem of turbulent flow around an airfoil, where we conclude that the approach can give performance that is superior to both fully explicit and fully implicit methods.