Computing corresponding values of the Neumann and Dirichlet boundary values for incompressible Stokes flow

Loustau, John; Bob-Egbe, Bolanle

doi:10.2140/involve.2010.3.459

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Computing corresponding values of the Neumann and Dirichlet boundary values for incompressible Stokes flow

John Loustau and Bolanle Bob-Egbe

Vol. 3 (2010), No. 4, 459–474

DOI: 10.2140/involve.2010.3.459

Abstract

We consider the Stokes equation for a flow through a partially obstructed channel and determine the relationship between Dirichlet boundary values (velocities) and Neumann boundary values (forces) for the FEM discrete form. For the steady state case we find a linear relationship. For the transient case the relationship depends on the time stepping procedure and includes the relationship at prior states. We resolve the issue for trapezoid and Adams–Bashford-2 time stepping. Since Stokes flow may be considered as the startup phase of Navier–Stokes flow, we give particular attention to a flow with a startup function.

Keywords

incompressible Stokes flow, finite element method, boundary values, computational fluid dynamics

Mathematical Subject Classification 2000

Primary: 47N40

Milestones

Received: 10 August 2007

Accepted: 23 October 2010

Published: 6 January 2011

Communicated by Kenneth S. Berenhaut

Authors

John Loustau
Department of Mathematics Hunter College (CUNY) New York, NY 11374 United States

Bolanle Bob-Egbe
Hunter College (CUNY) New York, NY 11374 United States

Vol. 3, No. 4, 2010