Numerical simulation of two-phase flow with imbedded interface of discontinuity is challenging in two major aspects. First, the interface can undergo change, merge and breakup during the course of the simulation. Examples of current successful methods in modeling flow with interface are, among others, the volume-of-fluid method, fronttracking method, and level-set method. Second, flow variables...

In addition to an overview of the immersed boundary/continuum methods and their finite element formulations, explicit vs. implicit and incompressible vs. compressible issues are discussed. The recent finite element formulations retain the same strategies employed in the original immersed boundary method, namely, the independent Lagrangian solid mesh moves on top of a fixed or prescribed backgro...

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...

In this paper the Immersed Boundary Method is presented, with some recent developments. The method is used to analyze fluid–structure interaction problems. Different aspects of the method are illustrated by applying it to blood flow in the heart and a flapping filament (flag-in-wind) problem.

The boundary slip error resulting from the interpolation/spreading non-reciprocity of direct-forcing immersed-boundary method is analyzed based on a simple and generic theoretical framework. In explicit implementations, scales with Courant number, as predicted by analysis confirmed lattice-Boltzmann simulation results. Using an analytical approximation error, force can be corrected in order to ...

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also invest...

The goal of this paper is to examine the evaluation of interfacial stresses using a standard, finite difference based, immersed boundary method (IMBM). This calculation is not trivial for two fundamental reasons. First, the immersed boundary is represented by a localized boundary force which is distributed to the underlying fluid grid by a discretized delta function. Second, this discretized de...