A Parallel-in-Time Navier-Stokes Solver Using Augmented Lagrangian Acceleration and Space-Time Multigrid Methods

Abstract

In this work we present a parallel-in-time solver of the Navier-Stokes equation for low Reynolds numbers. The solver uses an all-at-once Newton-Krylov method and the combination of Augmented Lagrangian and LSC preconditioning leading to embarrassingly parallel pressure solves. For the solution of the unsteady velocity system we compare multigrid waveform relaxation and space-time multigrid. For low and moderate Reynolds numbers this solver can improve the strong scalability compared to a time stepping solver. This method is also applied to a Carreau fluid showing the possible application in the area of transient simulation of polymer melts.