NDLI: Tether Force Constraints in Stokes Flow by the Immersed Boundary Method on a Periodic Domain

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Teran, Joseph M. Peskin, Charles S.
Copyright Year	2009
Abstract	The immersed boundary method is an algorithm for simulating the interaction of immersed elastic bodies or boundaries with a viscous incompressible fluid. The immersed elastic material is represented in the fluid equations by a system or field of applied forces. The particular case of Stokes flow with applied forces on a periodic domain involves two related mathematical complications. One of these is that an arbitrary constant vector may be added to the fluid velocity, and the other is the constraint that the integral of the applied force must be zero. Typically, forces defined on a freely floating elastic immersed boundary or body satisfy this constraint, but there are many important classes of forces that do not. For example, the so-called tether forces that are used to prescribe the simulated configuration of an immersed boundary, possibly in a time-dependent manner, typically do not sum to zero. Another type of force that does not have zero integral is a uniform force density that may be used to simulate an overall pressure gradient driving flow through a system. We present a method for periodic Stokes flow that when used with tether points, admits the use of all forces irrespective of their integral over the domain. A byproduct of this method is that the additive constant velocity associated with periodic Stokes flow is uniquely determined. Indeed, the additive constant is chosen at each time step so that the sum of the tether forces balances the sum of any other forces that may be applied.
Starting Page	3404
Ending Page	3416
Page Count	13
File Format	PDF
ISSN	10648275
DOI	10.1137/080720217
e-ISSN	10957197
Issue Number	5
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-08-14
Access Restriction	Subscribed
Subject Keyword	numerical methods Fluid-solid interactions immersed boundary method Stokes equations Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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