In this report, we propose a novel, massively parallelizable algorithm for the immersed boundary method based on the fluid solver of Guermond and Minev [11]. This solver employs a directional-splitting technique that allows the incompressible Navier–Stokes equation to be efficiently parallelized on both shared and distributed memory architectures. An implementation of the numerical scheme was c...

The immersed boundary method in its original formulation, introduced by Peskin in [9], exhibits a high degree of numerical stiffness. A finite element approach was proposed by Boffi et al. [1] and further developed in Boffi et al. [2,3] to solve some of the difficulties arising from the original formulation. We present a stability analysis for the two dimensional case with some numerical tests ...

A bifurcation occurs when an elastic filament rotates in a viscous fluid at frequency ω (bifurcation parameter). We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier–Stokes equations, and to determine the nature of the bifurcation, which turns out to be subcritical.

An efficient approach for the simulation of finite-size particles with interface resolution was presented by Uhlmann (J. Comput. Phys, Vol. 209, pp. 448-476, 2005). The present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability. An important step is a simple low-cost iterative procedure for the Euler-Lagrange coupling ...

The level set method commonly requires a reinitialization of the level set function due to interface motion and deformation. We extend the traditional technique for reinitializing the level set function to a method that preserves the interface gradient. The gradient of the level set function represents the stretching of the interface, which is of critical importance inmany physical applications...

In this paper, we present an immersed boundarymethod for modeling a contractile elastic ring in a three-dimensional Newtonian fluid. The governing equations are themodified Navier–Stokes equations with an elastic force from the contractile ring. The length of the elastic ring is time dependent and the ring shrinks with time because of its elastic nature in our proposed model. We dynamically red...

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...

Many problems involving internal interfaces can be formulated as partial differential equations with singular source terms. Numerical approximation to such problems on a regular grid necessitates suitable regularizations of delta functions. We study the convergence properties of such discretizations for constant coefficient elliptic problems using the immersed boundary method as an example. We ...

In this paper we outline a front-tracking method for computing the moving contact line. In particular, we are interested in the motion of two-dimensional drops and bubbles on a partially wetting surface exposed to shear flows. Peskin’s Immersed Boundary Method is used to model the liquid-gas interface, similar to the approach used by Unverdi and Traggvason. The movement near the moving contact ...

This study presents a methodology for modeling a developing turbulent boundary layer flows over surfaces with large (macro-scale) rougness elements, with particular application to flow over bio-fouled surfaces. A sharp-interface immersed boundary method coupled with a wall model and large-eddy simulations is used to carry out accurate simulations of flow over such macro-bio-fouled surfaces. Sim...