We present an Immersed Boundary method for interactions between elastic boundaries and mixtures of two fluids. Each fluid has its own velocity field and volume-fraction. A penalty method is used to enforce the condition that both fluids' velocities agree with that of the elastic boundaries. The method is applied to several problems: Taylor's swimming sheet problem for a mixture of two viscous f...

We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid equations is based on a standard staggered-grid approach. Fluid-body interaction is handled using Peskin's IB method; however, unlike existing IB approaches to such...

Explicit time discretizations of the Immersed Boundary method are known to require small timesteps to maintain stability. A number of implicit methods have been introduced to alleviate this restriction to allow for a more efficient method, but many of these methods still have a stability restriction on the timestep. Furthermore, almost no comparisons have appeared in the literature of the relat...

The immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a (visco-)elastic structure. In [M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1998; M...

The immersed boundary method is a practical and effective method for fluid–structure interaction problems. It has been applied to a variety of problems. Most of the timestepping schemes used in the method are explicit, which suffer a drawback in terms of stability and restriction on the time step. We propose a lattice Boltzmann based implicit immersed boundary method where the immersed boundary...

A projection-based immersed boundary method is dominated by sparse linear algebra routines. Using the open-source Cusp library, we observe a speedup (with respect to a single cpu core) which reflects the constraints of a bandwidth-dominated problem on the gpu. Nevertheless, gpus offer the capacity to solve large problems on commodity hardware. This work includes validation and a convergence stu...

The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluid-structure interaction. In the present work, we describe the application of the immersed boundary method to the simulation of the fluid dynamics of heart valves, including a model of a natural aortic valve and a model of a chorded prosthetic mitral valve. Each valve is m...

Historically, boundary fitted grids have been used to model complex geometries. The authors are investigating a novel grid generation concept, Immersed Boundary Method, as an improved methodology to boundary fitted grids. There are two significant disadvantages to using a boundary fitted grid. First, whether structured or unstructured, fitting a grid to a complex geometry prevents the use of si...

The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid. For some applications, such as modeling biological materials, capturing internal boundary viscosity is important. We present numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow. We find that t...