Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
Recently, it was understood how to repair a certain L2-orthogonality of
discretely-divergence-free vector fields and gradient fields such that the
velocity error of inf-sup stable discretizations for the incompressible
Stokes equations becomes pressure-independent. These new pressure-robust
Stokes discretizations deliver a small velocity error, whenever the
continuous velocity field can be well approximated on a given grid. On the
contrary, classical inf-sup stable Stokes discretizations can guarantee a
small velocity error only, when both the velocity and the pressure field can
be approximated well, simultaneously. In this contribution,
pressure-robustness is extended to the time-dependent Navier-Stokes
equations. In particular, steady and time-dependent potential flows are shown
to build an entire class of benchmarks, where pressure-robust discretizations
can outperform classical approaches significantly. Speedups will be explained
by a new theoretical concept, the discrete Helmholtz projector of an inf-sup
stable discretization. Moreover, different discrete nonlinear convection
terms are discussed, and skew-symmetric pressure-robust discretizations are
proposed