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Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
| Venue: | J Comput Phys |
| Citations: | 73 - 9 self |
BibTeX
@ARTICLE{Zhu_simulationof,
author = {Luoding Zhu and Charles S. Peskin},
title = {Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method},
journal = {J Comput Phys},
year = {}
}
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Abstract
This paper reports the computer simulation of a flapping flexible filament in a flowing soap film using the immersed boundary method. Our mathematical formu-lation includes filament mass and elasticity, gravity, air resistance, and the two wires that bound the flowing soap film. The incompressible viscous Navier–Stokes equa-tions, which are used to describe the motion of the soap film and filament in our formulation, are discretized on a fixed uniform Eulerian lattice while the filament equations are discretized on a moving Lagrangian array of points which do not nec-essarily coincide with the fixed Eulerian mesh points of the fluid computation. The interaction between the filament and the soap film is handled by a smoothed ap-proximation to the Dirac delta function. This delta function approximation is used not only to interpolate the fluid velocity and to apply force to the fluid (as is com-monly done in immersed boundary computations), but also to handle the mass of the filament, which is represented in our calculation as delta function layer of fluid mass density supported along the immersed filament. Because of this nonuniform density, we need to use a multigrid method for solving the discretized fluid equations.
Keyphrases
immersed boundary method flapping flexible filament flowing soap film soap film lagrangian array fluid velocity filament equation fixed eulerian mesh point fluid computation nonuniform density dirac delta function air resistance multigrid method filament mass incompressible viscous navier stokes equa-tions delta function layer computer simulation immersed boundary computation delta function approximation fluid equation smoothed ap-proximation fixed uniform eulerian lattice mathematical formu-lation immersed filament fluid mass density
