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A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations

Published online by Cambridge University Press:  09 August 2018

Qinghai Zhang ,
Robert D. Guy  and
Bobby Philip
Qinghai Zhang*
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA.
Robert D. Guy*
Affiliation:
Department of Mathematics, University of California Davis, Davis, CA 95616, USA.
Bobby Philip*
Affiliation:
Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
*
*Corresponding author.Email address:qinghai@math.utah.edu
Email: guy@math.ucdavis.edu
Email: philipb@ornl.gov
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Abstract

This paper presents a method for solving the linear semi-implicit immersed boundary equations which avoids the severe time step restriction presented by explicit-time methods. The Lagrangian variables are eliminated via a Schur complement to form a purely Eulerian saddle point system, which is preconditioned by a projection operator and then solved by a Krylov subspace method. From the viewpoint of projection methods, we derive an ideal preconditioner for the saddle point problem and compare the efficiency of a number of simpler preconditioners that approximate this perfect one. For low Reynolds number and high stiffness, one particular projection preconditioner yields an efficiency improvement of the explicit IB method by a factor around thirty. Substantial speed-ups over explicit-time method are achieved for Reynolds number below 100. This speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.

Keywords

65M5565F0876M2076D99Fluid-structure interactionimmersed boundary methodprojection methodpreconditioning
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 4 , November 2014 , pp. 473 - 498
Copyright
Copyright © Global Science Press Limited 2014

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