Implementation and Analysis of a Prototype Implicit, Matrix-Free, DGSEM Solver for LES

Abstract

This Masters thesis explores the usage of a matrix-free GMRES solver for implicit time integration of unsteady turbulent flows using a high-order DGSEM spatial discretisation. Efficient time integration methods remain one of the main challenges towards enabling industrial usage of high-order methods to perform scale resolving simulations. The focus on the study is on the development of such a prototype implicit solver for the DGSEM solver in CFD framework TRACE developed by DLR specialised at internal aerodynamics of turbomachinery components. To gain a fundamental understanding of the method, and have a lightweight experimenting tool, a 1D DGSEM solver was first developed from scratch. With this gained knowledge, implementation of the solver in TRACE could start. The prototype solver developed in TRACE is able to use both finite-difference and forward automatic differentiation techniques to enable the matrix-free GMRES method. After successful verification and validation of the solver, it was applied to perform an LES of a turbulent channel flow. The implicit solver showcased similar results compared to the time-explicit reference simulations, at time step sizes greater than the explicit limit. The implicit solver was also found to require less CPU hours than the explicit reference simulations.