We present an investigation of a boundary condition algorithm for the lattice Boltzmann method, which introduces Dirichlet conditions on velocity using a singular force applied on the fluid-solid interface (immersed boundary method). The algorithm has been proposed in the literature in different versions and mainly numerically tested, only in specific cases. An approach based on a generalized a...

In this paper, we present an immersed boundary (IB) method to simulate a dry foam, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquidfilm internal boundaries that partition the gas into discrete cells or bubbles. The liquid film boundaries are flexible, contract under the influence of ...

The jump is defined as [∇u · n] = ∇u · n +∇u ·n where u = u|Ω± and n is the unit outward pointing normal to Ω (see figure 1). Also, we denote [u] = u − u. Many numerical methods have been developed for problem (1.1). Perhaps the most notable ones are the finite difference method of Peskin [18] (i.e., immersed boundary method) and the method of LeVeque and Li [11] (i.e., the immersed interface m...

A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present methodimplements the conservation laws in all cells ...

ACKNOWLEDGMENTS I have had two wonderful years at Vanderbilt University. I would like to use this chance to express my gratitude to those who have helped me during this period of time. First, I want to thank my advisor, Dr. Haoxiang Luo. His support and wealth of knowledge guided me through the obstacles in my research. He was also willing to share his experience as a graduate student with me t...

We present an automatic animation system for jellyfish that is based on a physical simulation. We model the thrust of an adult jellyfish, and the organism’s morphology in its most active mode of locomotion. We reduce our model by considering only species that are axially symmetric so that we can approximate the full 3D geometry of a jellyfish with a 2D simulation. We simulate the organism’s ela...

The immersed boundary (IB) method is a mathematical formulation for fluid-structure interaction problems, where immersed incompressible visco-elastic bodies or boundaries interact with an incompressible fluid. The original numerical scheme associated to the IB method requires a smoothed approximation of the Dirac delta distribution to link the moving Lagrangian domain with the fixed Eulerian on...

This paper presents an efficient treatment of fluid/elastic–structure interactions that takes advantage of the Fourier representation of immersed boundaries. We assume that the fluid is incompressible with uniform density and viscosity and that the immersed boundaries have fixed topologies. These elastic bodies can have large deformations and evolve anywhere within the fluid domain. They may be...

In this paper, we investigate the stability of a fluid-structure interaction problem in which a flexible elastic membrane immersed in a fluid is excited via periodic variations in the elastic stiffness parameter. This model can be viewed as a prototype for active biological tissues such as the basilar membrane in the inner ear, or heart muscle fibers immersed in blood. Problems such as this, in...