We develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semi-implicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the projection method to solve the fluid equations, the pressure is decoupled and we have a symmetric positive d...

Among other things, we prove the following two topologcal statements about closed hyperbolic 3-manifolds. First, every rational second homology class of a closed hyperbolic 3-manifold has a positve integral multiple represented by an oriented connected closed π1-injectively immersed quasiFuchsian subsurface. Second, every rationally null-homologous, π1-injectively immersed oriented closed 1-sub...

We present a Direct Forcing (DF) approach for simulations of flows over moving bodies, on Cartesian grids, capable of reducing the amplitude of the force oscillations, by using a regularized approach.

In this paper, we present a consistent and rigorous derivation of some stochastic fluid-structure interaction models based on an implicit interface formulation of the stochastic immersed boundary method. Based on the fluctuation-dissipation theorem, a proper form can be derived for the noise term to be incorporated into the deterministic hydrodynamic fluid-structure interaction models in either...

The purpose of the study is to investigate the wind noise reduction provided by microphone windscreens at different frequencies of the impinging turbulence. The windscreen is assumed to be a cylindrically shaped porous medium. This paper uses a high-order scheme to improve the accuracy at the interface between air and porous medium. The computational scheme is based on a modified immersed-bound...

A twisted elastic rod with intrinsic curvature is considered. We investigate the dynamics of the rod in a viscous incompressible fluid. This fluid is governed by the Navier–Stokes equations and the fluid-rod interaction problem is solved by the generalized immersed boundary method combined with the Kirchhoff rod theory. We classify the equilibrium configurations of an open elastic rod as they d...

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 ...

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...