PDE Seminar

Title: Convergence proof of a Stokes flow immersed boundary method
Speaker: Professor Yoichiro Mori
Speaker Info: University of British Columbia
Brief Description:
Special Note:

The immersed boundary method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. It makes use of a regular Cartesian fluid grid and a Lagrangian curvilinear mesh to represent the elastic structure. A prinicipal algorithmic step is to find the solution of the fluid equations with a singular external force field. The singular force field, supported on a manifold of codimension 1 (the immersed boundary), is regularized using discrete delta functions so that the underlying fluid grid can "feel" its presence. This regularized singular force field is then used as the right-hand side of the discretized fluid equations to solve for the fluid velocity. Such regularizations are used not only in the context of the immersed boundary method but also in level set methods and front-tracking methods. In this talk, I will outline a proof of convergence of a stationary immersed boundary problem for two-dimensional periodic Stokes flow. A key to the proof is an estimate on the difference between the discrete and continuous Green's function. We obtain both pointwise and uniform error estimates to prove that the solution converges up to the immersed boundary. We demonstrate computational examples to show that the error estimates capture the overall features of the convergence rates.

Date: Thursday, May 03, 2007
Time: 4:10pm
Where: Lunt 105
Contact Person: Prof. Gui-Qiang Chen
Contact email: gqchen@math.northwestern.edu
Contact Phone: 847-491-5553
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