Convergence proof of the velocity field for a stokes flow immersed boundary method |
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Authors: | Yoichiro Mori |
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Institution: | University of British Columbia, Department of Mathematics, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada |
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Abstract: | The immersed boundary (IB) method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. It is characterized by the use of a uniform Cartesian mesh for the fluid, a Lagrangian curvilinear mesh on the elastic material, and discrete delta functions for communication between the two grids. We consider a simple IB problem in a two‐dimensional periodic fluid domain with a one‐dimensional force generator. We obtain error estimates for the velocity field of the IB solution for the stationary Stokes problem. We use this result to prove convergence of a simple small‐amplitude dynamic problem. We test our error estimates against computational experiments. © 2007 Wiley Periodicals, Inc. |
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