We study the focusing properties of a two dimensional complex square-lattice photonic crystal (PC) comprising air holes immersed in Ge medium. The finite difference time domain (FDTD) method is utilized to calculate the dispersion band diagram and to simulate the image formation incorporating the perfectly matched layer (PML) boundary condition. In contrast to the common square PCs with the sam...

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...

In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems. We simulate the fluid-structure interaction and separation process using the immersed boundary method. In these simulations we model and simulate different density and viscosity values of the biofilm than that of the surrounding fluid. The simulation also includes breakable springs connecting...

In this paper, we develop an immersed boundary lattice Boltzmann approach to simulate deformable capsules in flows. The lattice Boltzmann method is utilized to solve the incompressible flow field over a regular Eulerian grid, while the immersed boundary method is employed to incorporate the fluid–membrane interaction with a Lagrangian representation of the capsule membrane. This algorithm was v...

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...

This communication describes the results of bubble rise simulations using a lattice Boltzmann method and a front-tracking finite-difference method. The simulations, performed in a 2-D periodic box, consider two specific examples: a steadily rising bubble and a bubble rising in an oscillatory manner with accompanying shape change. We compare the shapes and rise velocities of the steadily rising ...

This work presents an immersed boundary–lattice Boltzmann method for free-swimming sperms in an incompressible viscous fluid. This method involves sperm model, fluid solver and fluid– structure interaction (FSI). The sperm is simplified as a nonlinear beam. To drive the swimming motion, an internal moment is introduced into the beam equation. The fluid dynamics is obtained by solving the lattic...

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmannmethod. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have b...

If we consider a finite difference method simply as a set of equations containing a small parameter (the grid spacing), it is evident that the tools of asymptotic analysis can give us useful information about the method. The applicability of this approach for studying consistency, long time behavior and stability is demonstrated. As example, we use a simple lattice Boltzmann scheme for the 1D a...