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.
Citation
John Loustau. Bolanle Bob-Egbe. "Computing corresponding values of the Neumann and Dirichlet boundary values for incompressible Stokes flow." Involve 3 (4) 459 - 474, 2010. https://doi.org/10.2140/involve.2010.3.459
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