A multigrid method for a model of the implicit immersed boundary equations

Journal Article · Sun Jan 01 04:00:00 EST 2012 · Communications in Computational Physics

DOI:https://doi.org/10.4208/cicp.010211.070711s· OSTI ID:1037648

Guy, Robert ^[1]; Philip, Bobby ^[2]

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1. University of California, Davis
2. ORNL

Explicit time stepping schemes for the immersed boundary method require very small time steps in order to maintain stability. Solving the equations that arise from an implicit discretization is difficult. Recently, several different approaches have been proposed, but a complete understanding of this problem is still emerging. A multigrid method is developed and explored for solving the equations in an implicit time discretization of a model of the immersed boundary equations. The model problem consists of a scalar Poisson equation with conformation-dependent singular forces on an immersed boundary. This model does not include the inertial terms or the incompressibility constraint. The method is more efficient than an explicit method, but the efficiency gain is limited. The multigrid method alone may not be an effective solver, but when used as a preconditioner for Krylov methods, the speed-up over the explicit time method is substantial. For example, depending on the constitutive law for the boundary force, with a time step 100 times larger than the explicit method, the implicit method is about 15-100 times more efficient than the explicit method. A very attractive feature of this method is that the efficiency of the multigrid preconditioned Krylov solver is shown to be independent of the number of immersed boundary points.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: ME USDOE - Office of Management, Budget, and Evaluation; ORNL work for others
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1037648
• Journal Information: Communications in Computational Physics, Journal Name: Communications in Computational Physics Journal Issue: 2 Vol. 12; ISSN 1815-2406
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EFFICIENCY
FLUID-STRUCTURE INTERACTIONS
POISSON EQUATION
SCALARS
STABILITY