A Parallel Multigrid Solver for Time-Periodic Incompressible Navier-Stokes Equations in 3D

In this talk, we consider the efficient solution of the discrete and nonlinear systems arising from the discretization of the Navier-Stokes equations with Finite Differences. In particular we study the incompressible, unsteady Navier-Stokes equations with periodic boundary condition in time. Our approach is based on a space-time multigrid method, which allows for parallelization in space as well as in time. Clearly, the traditionally sequential time integration a limits the parallelism of the solver to the spatial variables and can therefore be an obstacle to parallel scalability. On the other hand the time periodicity allows for a space-time discretization, which adds time as an additional direction for parallelism and thus allows for much better parallel scalability. However, as the structure of the non-linear system to be solved is changed by the simultaneous parallelization in space and time, particular care has to be taken on the side of the solution method. Here, to achieve fast convergence, a space-time multigrid algorithm is developed, which is employed after linearization of the convective term. As an important ingredient of the multigrid method the SCGS smoothing procedure (Symmetrical Collective Gauss–Seidel relaxation, a.k.a. box smoothing) proposed by S. P. Vanka, for the steady viscous incompressible Navier–Stokes equations is extended to the unsteady case and its properties are studied using local Fourier analysis. We present numerical experiments to analyze the scalability and the convergence of the multigrid algorithm, focusing on the case of a pulsatile flow. Powered by TCPDF (www.tcpdf.org)