he last decade has seen a tremendous rise in the popularity of immersed boundary methods [1-6] . The primary factor driving this is the relative ease with which this methodology allows researchers to develop computational models of flows with complex geometries and/or moving boundaries. Immersed boundary solvers have been employed successfully for simulating biological flows, physiological flow...

Mathematical modelling provides a useful framework within which to investigate 4 the organization of biological tissues. With advances in experimental biology leading to increasingly 5 detailed descriptions of cellular behaviour, models that consider cells as individual objects are be6 coming a common tool to study how processes at the single-cell level affect collective dynamics and 7 determin...

We present numerical simulations of active fluid droplets immersed in an external fluid in 2-dimensions using an Immersed Boundary method to simulate the fluid droplet interface as a Lagrangian mesh. We present results from two example systems, firstly an active isotropic fluid boundary consisting of particles that can bind and unbind from the interface and generate surface tension gradients th...

The application of the Immersed Boundary ~IB! method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard Reynolds-Averaged Navier-Stokes models or the more so...

For simulating rarefied gas flows around a moving body, an immersed boundary method is presented here in conjunction with the Direct Simulation Monte Carlo (DSMC) method in order to allow the movement of a three dimensional immersed body on top of a fixed background grid. The simulated DSMC particles are reflected exactly at the landing points on the surface of the moving immersed body, while t...

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...

We present a second-order accurate version of the Immersed Boundary Projection Method for imposing Dirichlet boundary conditions at irregular boundaries while using a Cartesian grid and a standard discretization, applicable to elliptic and parabolic PDEs. No modi cation to the stencil is required. Rather, boundary conditions are enforced by applying a force at the boundary that is unknown a pri...

In this paper, we present a combined immersed-boundary/ghost-fluid sharp interface method for the simulations of three-dimensional two-phase flows interacting with moving bodies on fixed Cartesian grids. This work is based on a sharp interface immersed boundary method for fluid flows interacting with moving bodies and a level set based ghost fluid method (GFM) for two-phase interface treatment....

We propose a fast and non-stiff approach for the solutions of the Immersed Boundary Method, for Newtonian, incompressible flows in two or three dimensions. The proposed methodology is built on a robust semi-implicit discretization introduced by Peskin in the late 70’s which is solved efficiently through the novel use of a fast, treecode strategy to compute flow-structure interactions. Optimal m...

A modified immersed-boundary method is developed using the direct-forcing concept. An improved bilinear interpolation/extrapolation algorithm is implemented for more accurate boundary forcing expressions and easier implementation. Detailed discussions of the method are presented on the stability, velocity interpolation on the immersed boundary, directforcing extrapolation to the grid points, re...