A computational model of aquatic animal locomotion
Journal of Computational Physics
Journal of Computational Physics
Stability analysis for the immersed fiber problem
SIAM Journal on Applied Mathematics
Simulating the motion of flexible pulp fibres using the immersed boundary method
Journal of Computational Physics
An adaptive version of 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
The Method of Regularized Stokeslets
SIAM Journal on Scientific Computing
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
Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
Journal of Computational Physics
Analysis and computation of immersed boundaries, with application to pulp fibres
Analysis and computation of immersed boundaries, with application to pulp fibres
Simulating the dynamics and interactions of flexible fibers in Stokes flows
Journal of Computational Physics
Simulations of the Whirling Instability by the Immersed Boundary Method
SIAM Journal on Scientific Computing
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
A multirate time integrator for regularized Stokeslets
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
We test the efficacy of using a single Lagrangian point to represent a sphere, and a one-dimensional array of such points to represent a slender body, in a new immersed boundary method for Stokes flow. A numerical parameter, the spacing of the Eulerian grid, is used to determine the effective radius of the immersed sphere or slender body. Such representations are much less expensive computationally than those with two or three-dimensional meshes of Lagrangian points. To perform this test, we develop a numerical method to solve the discretized Stokes equations on an unbounded Eulerian grid which contains an arbitrary configuration of Lagrangian points that apply force to the fluid and that move with the fluid. We compare results computed with this new immersed boundary method to known results for spheres and rigid cylinders in Stokes flow in R^3. We find that, for certain choices of parameters, the interactions with the fluid of a single Lagrangian point accurately replicate those of a sphere of some particular radius, independent of the location of the point with respect to the Eulerian grid. The interactions of a linear array of Lagrangian points, for certain choices of parameters, accurately replicate those of a cylinder of some particular radius, independent of the position and orientation of the array with respect to the Eulerian grid. The effective radius of the sphere and the effective radius of the cylinder turn out to be related in a simple and natural way. Our results suggest recipes for choosing parameters that should be useful to practitioners. One surprising result is that one must not use too many Lagrangian points in an array. Another is that the approximate delta functions traditionally used in the immersed boundary method perform much better than higher order delta functions with the same support.