Speaker: Nicholas Chisholm
Title: A Novel Approach to Regularizing Stokeslets via Smoothed Vector Potentials
Abstract: The method of regularized Stokeslets is well suited to simulating complex, micro-scale fluid phenomena. We introduce the Stokes equation, its associated boundary integral equation, and its approximate solution using regularized fundamental solutions (or regularized 'Stokeslets'). We implement a novel approach to regularizing the Stokeslet; we first consider the "vector potential" of the Stokeslet and regularize that quantity instead, which produces a regularized fluid flow that automatically satisfies the fluid incompressibility condition. Moreover, the regularization can be chosen such that the Stokeslet is equivalent (or arbitrarily close) to the original, singular Stokeslet outside a small region surrounding the point of forcing. Regularized Stokeslets having this latter property may be especially useful for dealing with flows bounded by surrounding cavities or walls. We validate the usefulness of our regularization approach for well-known problems such as flow due to a translating sphere. Our eventual goal is to take advantage of our progress in the method of regularized Stokeslets to simulate forces and fluid flows during active cellular processes such as mitosis.
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