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Title: A projection preconditioner for solving the implicit immersed boundary equations

Abstract

This study 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. In conclusion, this speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.

Authors:
 [1];  [2];  [3]
  1. Univ. of Utah, Salt Lake City, UT (United States). Department of Mathematics
  2. University of California Davis, Davis, CA (United States). Department ofMathematics
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE; USDOE Office of Management, Budget, and Evaluation; Work for Others (WFO)
OSTI Identifier:
1265332
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article
Journal Name:
Numerical Mathematics: Theory, Methods and Applications
Additional Journal Information:
Journal Volume: 7; Journal Issue: 4; Journal ID: ISSN 1004-8979
Publisher:
Global Science Press
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING

Citation Formats

Zhang, Qinghai, Guy, Robert D., and Philip, Bobby. A projection preconditioner for solving the implicit immersed boundary equations. United States: N. p., 2014. Web.
Zhang, Qinghai, Guy, Robert D., & Philip, Bobby. A projection preconditioner for solving the implicit immersed boundary equations. United States.
Zhang, Qinghai, Guy, Robert D., and Philip, Bobby. Sat . "A projection preconditioner for solving the implicit immersed boundary equations". United States.
@article{osti_1265332,
title = {A projection preconditioner for solving the implicit immersed boundary equations},
author = {Zhang, Qinghai and Guy, Robert D. and Philip, Bobby},
abstractNote = {This study 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. In conclusion, this speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.},
doi = {},
journal = {Numerical Mathematics: Theory, Methods and Applications},
issn = {1004-8979},
number = 4,
volume = 7,
place = {United States},
year = {2014},
month = {11}
}