Tóm tắt
This paper is concerned with the mathematical structure of the immersed
boundary (IB) method, which is intended for the computer simulation of
fluid–structure interaction, especially in biological fluid dynamics. The IB
formulation of such problems, derived here from the principle of least action,
involves both Eulerian and Lagrangian variables, linked by the Dirac
delta function. Spatial discretization of the IB equations is based on a fixed
Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for
the Lagrangian variables. The two types of variables are linked by interaction
equations that involve a smoothed approximation to the Dirac delta function.
Eulerian/Lagrangian identities govern the transfer of data from one mesh to
the other. Temporal discretization is by a second-order Runge–Kutta method.
Current and future research directions are pointed out, and applications of
the IB method are briefly discussed.
