2002/01/01 by Charles S. Peskin · 3,744 citations
Engineering · Mathematics · #Action (physics) #Applied mathematics #Boundary (topology) #Boundary value problem #Cartesian coordinate system #Classical mechanics #Computer science #Curvilinear coordinates #Dirac delta function #Discretization #Eulerian path #Finite element method #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Fluid–structure interaction #Geometry #Immersed boundary method #Lagrangian #Lagrangian and Eulerian specification of the flow field #Lattice Boltzmann Simulation Studies #Mathematical analysis #Mathematics #Physics #Principle of least action
paper · pdf · doi:10.1017/s0962492902000077
published in Acta Numerica 11, 479-517 (Cambridge University Press (CUP))
crossref issued 2002/01/01 · crossref published 2002/01/01 · crossref published-print 2002/01/01 · openalex publication_date 2002/01/01 · crossref created 2002/07/28 · crossref published-online 2003/07/15 · crossref deposited 2019/06/06 · openalex created_date 2025/10/10 · crossref indexed 2026/08/06 · openalex updated_date 2026/08/08
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.