The immersed boundary method is an approach – in computational fluid dynamics – to model and simulate mechanical systems in which elastic structures (or membranes) interact with fluid flows. Treating the coupling (the elastic boundary changes the flow of the fluid and the fluid moves the elastic boundary simultaneously) of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations. In the immersed boundary method approach the fluid is represented in an Eulerian coordinate frame and the structures in a Lagrangian coordinate frame. For Newtonian fluids governed by the Navier–Stokes equations the immersed boundary method fluid equations are

with incompressibility condition

The immersed structures are typically represented by a collection of interacting particles Zj with a prescribed force law, where Fj is the force acting on the jth particle. The forces are accounted for in the fluid equations by the force density

where δa is an approximation of the Dirac δ-function smoothed out over a length scale a. The immersed structures are then updated using the equation

Variants of this basic approach have been applied to simulate a wide variety of mechanical systems involving elastic structures which interact with fluid flows.

C. S. Peskin, The immersed boundary method, Acta Numerica, 11, pp. 1–39, 2002.

详细内容可以参见 C. S. Peskin 教授的个人网页： http://www.math.nyu.edu/faculty/peskin/

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