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A fast, robust, and non-stiff Immersed Boundary Hector D. Ceniceros
 

Summary: A fast, robust, and non-stiff Immersed Boundary
Method
Hector D. Ceniceros
Department of Mathematics, University of California Santa Barbara, CA 93106
Jordan E. Fisher
Department of Mathematics, University of California Santa Barbara, CA 93106
Abstract
We propose a fast and non-stiff approach for the solutions of the Immersed
Boundary Method, for Newtonian, incompressible flows in two or three di-
mensions. The proposed methodology is built on a robust semi-implicit dis-
cretization introduced by Peskin in the late 70's which is solved efficiently
through the novel use of a fast, treecode strategy to compute flow-structure
interactions. Optimal multipole-type expansions are performed numerically
by solving a least squares problem with a new, fast iterative algorithm.
The new Immersed Boundary Method is particularly well suited for three-
dimensional applications and/or for problems where the number of immersed
boundary points is large. We demonstrate the efficacy and superiority of the
method over existing approaches with two simple but illustrative examples
in 3D.
Keywords: semi-implicit method, Navier-Stokes equations, treecode,

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics