A computational model of aquatic animal locomotion
Journal of Computational Physics
Journal of Computational Physics
Interaction of oscillating filaments: a computational study
Journal of Computational Physics
A numerical method for suspension flow
Journal of Computational Physics
A computational model of the cochlea using the immersed boundary method
Journal of Computational Physics
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
An analysis of the fractional step method
Journal of Computational Physics
Projection method I: convergence and numerical boundary layers
SIAM Journal on Numerical Analysis
Projection Method II: Godunov--Ryabenki Analysis
SIAM Journal on Numerical Analysis
The Journal of Supercomputing - Special issue on supercomputing in medicine
Modeling visoelastic networks and cell deformation in the context of the immersed boundary method
Journal of Computational Physics
Simulating the motion of flexible pulp fibres using the immersed boundary method
Journal of Computational Physics
Modeling arteriolar flow and mass transport using the immersed boundary method
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Two-Dimensional Simulations of Valveless Pumping Using the Immersed Boundary Method
SIAM Journal on Scientific Computing
A three-dimensional computer model of the human heart for studying cardiac fluid dynamics
ACM SIGGRAPH Computer Graphics
A three-dimensional computer model for fluid flow through a collapsible tube
A three-dimensional computer model for fluid flow through a collapsible tube
Lattice-Based Flow Field Modeling
IEEE Transactions on Visualization and Computer Graphics
Coupling water and smoke to thin deformable and rigid shells
ACM SIGGRAPH 2005 Papers
A DLM/FD method for fluid/flexible-body interactions
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
A fictitious domain method for particulate flows with heat transfer
Journal of Computational Physics
Unconditionally stable discretizations of the immersed boundary equations
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
Comparison of various fluid-structure interaction methods for deformable bodies
Computers and Structures
Simulation of flexible filaments in a uniform flow by the immersed boundary method
Journal of Computational Physics
On the stability of the finite element immersed boundary method
Computers and Structures
Journal of Computational Physics
Journal of Computational Physics
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Simulating the dynamics of flexible bodies and vortex sheets
Journal of Computational Physics
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
Journal of Computational Physics
An improved penalty immersed boundary method for fluid-flexible body interaction
Journal of Computational Physics
Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Computational Physics
An immersed boundary energy-based method for incompressible viscoelasticity
Journal of Computational Physics
A Weak Formulation of the Immersed Boundary Method
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
On numerical modeling of animal swimming and flight
Computational Mechanics
Computers & Mathematics with Applications
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This paper reports the computer simulation of a flapping flexible filament in a flowing soap film using the immersed boundary method. Our mathematical formulation includes filament mass and elasticity, gravity, air resistance, and the two wires that bound the flowing soap film. The incompressible viscous Navier-Stokes equations, 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 necessarily 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 approximation 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 commonly 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. This replaces the FFT-based method that is commonly used in the uniform-density case. Our main results are as follows. (i) The sustained flapping of the filament only occurs when filament mass is included in the formulation of the model; within a certain range of mass, the more the mass of the filament, the bigger the amplitude of the flapping. (ii) When the length of filament is short enough (below some critical length), the filament always approaches its straight (rest) state, in which the filament points downstream; but when the length is larger, the system is bistable, which means that it can settle into either state (rest state or sustained flapping) depending on the initial conditions. This numerical result we observed in computer simulation is the same as that of the laboratory experiment even though the Reynolds number of the computations is lower than that of the laboratory experiment by two orders of magnitude.