Pressure boundary conditions, projection methods and <br/><br/>finite-element computations

Thursday, February 25, 2010 - 9:00am - 9:45am
EE/CS 3-180
Robert Pego (Carnegie-Mellon University)
Keywords: Time-dependent incompressible viscous flow, stable discretization, time splitting, Stokes pressure, Leray projection.

Abstract: How to properly specify boundary conditions for pressure for
no-slip incompressible viscous flow has been a longstanding issue
in analysis and computation. A recent analytical resolution of
this issue is based on a local well-posedness theorem for an
extended Navier-Stokes dynamics, in which the zero-divergence
condition is replaced by a pressure formula that involves the
commutator of the Laplacian and Leray projection operators.
I'll indicate progress on some related analytical questions
(domains with corners, MHD), but will focus on improvements in
numerical schemes that involve projection methods in time and
finite elements in space. We find schemes that involve simple
kinds of finite elements (Lagrange of equal order for velocity
and pressure, including piecewise-linear, for example) that are
stable in tests with large time steps at low Reynolds number,
with up to 3rd-order accuracy in time for both velocity and
pressure. Notably, these schemes do not include projection
methods that update the pressure from previous steps.
MSC Code: