Performance Analysis of Parallel Schwarz Preconditioners in the LES of Turbulent Channel Flows

We present a comparative study of parallel Schwarz preconditioners in the solution of linear systems arising in a Large Eddy Simulation (LES) procedure for turbulent plane channel flows. This procedure applies a time-splitting technique to suitably filtered Navier-Stokes equations, in order to decouple the continuity and momentum equations, and uses a semi-implicit scheme for time integration and finite volumes for space discretisation. This approach requires the solution of four sparse linear systems at each time step, accounting for a large part of the overall simulation; hence the linear system solvers are a crucial component in the whole procedure. Several preconditioners are applied in the simulation of a reference test case for the LES community, using discretisation grids of different sizes, with the aim of analysing the effects of different algorithmic choices defining the preconditioners, and identifying the most effective ones for the selected problem. The preconditioners, coupled with the GMRES method, are run within SParC-LES, a recently developed LES code based on the PSBLAS and MLD2P4 libraries for parallel sparse matrix computations and preconditioning.