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...

Abstract. The Immersed Boundary Method (IBM) has been designed by Peskin for the modeling and the numerical approximation of fluid-structure interaction problems. Recently, a finite element version of the IBM as been developed, which offers interesting features for both the analysis of the problem under consideration and the robustness and flexibility of the numerical scheme. In this paper we s...

background: the airway surface liquid (asl), which is a fluid layer coating the interior epithelial surface of the bronchi and bronchiolesis, plays an important defensive role against foreign particles and chemicals entering lungs. objective: numerical investigation has been employed to solve two-layer model consisting of mucus layer as a viscoelastic fluid and periciliary liquid layer as a newt...

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 ...

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...