A projection preconditioner for solving the implicit immersed boundary equations

Journal Article · Sat Nov 01 04:00:00 EDT 2014 · Numerical Mathematics: Theory, Methods and Applications

OSTI ID:1265332

Zhang, Qinghai ^[1]; Guy, Robert D. ^[2]; Philip, Bobby ^[3]

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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)

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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE; USDOE Office of Management, Budget, and Evaluation; ORNL work for others
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1265332
• Journal Information: Numerical Mathematics: Theory, Methods and Applications, Journal Name: Numerical Mathematics: Theory, Methods and Applications Journal Issue: 4 Vol. 7; ISSN 1004-8979
• Publisher: Global Science Press
• Country of Publication: United States
• Language: English

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