Navier-Stokes equation

Reynolds-robust preconditioners for the stationary incompressible Navier--Stokes equations

Prof.Patrick Farrell, University of Oxford

Dec 5, 12:00 - 13:00

B9 L2 R2322 H1

Navier-Stokes equation Robustness

Building on the work of Schöberl, Olshanskii, and Benzi, in this talk we present the first preconditioner for the Newton linearization of the stationary Navier--Stokes equations in three dimensions that achieve both optimal complexity in of count and Reynolds-robustness. The exact details of the preconditioner varies with discretization, but the general theme is to combine augmented Lagrangian stabilisation, a custom multigrid prolongation operator involving local solves on coarse cells, and an additive patchwise relaxation on each level that captures the kernel of the divergence operator.