Immersed boundary methods have been widely used for simulating flows with complex geometries, as quality boundaryconforming grids are usually difficult to generate for complex geometries, especially, when motion and/or deformation is involved. Complex geometries can be conveniently represented using triangulated surfaces in a Lagrangian manner. A major task in immersed boundary simulations is t...

Consider a strictly convex bounded regular domain C of R. In this paper we construct complete properly immersed in C minimal surfaces with boundary. Our examples have arbitrary finite topology. We also prove that complete properly immersed in C minimal surfaces with boundary are dense in the space of properly immersed in C minimal surfaces with boundary, endowed with the topology of the Hausdor...

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 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...

A new sharp-interface immersed boundary method based approach for the computation of low-Mach number flow-induced sound around complex geometries is described. The underlying approach is based on a hydrodynamic/acoustic splitting technique where the incompressible flow is first computed using a second-order accurate immersed boundary solver. This is followed by the computation of sound using th...

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...

The thesis presents an analysis of the continuous forcing approach of the immersed boundary method for the simulation of the interaction between uid and rigid particles in combination with the single relaxation lattice Boltzmann method. The immersed boundary method as a numerical algorithm is implemented in the context of two massively parallel software frameworks (waLBerla and pe) developed at...

For the figure eight knot, we show that slopes with even numerator are slopes of immersed surfaces covered by incompressible, boundary-incompressible embeddings in some finite cover.  2000 Elsevier Science B.V. All rights reserved.

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...