In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions.
Spring forces, bending resistance or any other type of behavior can be built into this term.
The force exerted by the structure on the fluid is then interpolated as a source term in the momentum equation using where
The forcing can be extended to multiple dimensions to model elastic surfaces or three-dimensional solids.
Assuming a massless structure, the elastic fiber moves with the local fluid velocity and can be interpolated via the delta function where
Variants of this basic approach have been applied to simulate a wide variety of mechanical systems involving elastic structures which interact with fluid flows.
These include stochastic formulations for microscopic systems, viscoelastic soft materials, complex fluids, such as the Stochastic Immersed Boundary Methods of Atzberger, Kramer, and Peskin,[2][3] methods for simulating flows over complicated immersed solid bodies on grids that do not conform to the surface of the body Mittal and Iaccarino,[4] and other approaches that incorporate mass and rotational degrees of freedom Olson, Lim, Cortez.