Moving boundaries in micro-scale biofluid dynamics

SUMMARYThe volume of uid (VOF) and immersed boundary (IB) methods are two popular computational techniques for multi-uid dynamics. To help shed light on the performance of both techniques, we present accuracy assessment, which includes interfacial geometry, detailed and global uid ow characteristics, and computational robustness. The investigation includes the simulations of a droplet under static equilibrium as a limiting test case and a droplet rising due to gravity for Re61000. Surface tension force models are key issues in both VOF and IB and alternative treatments are examined resulting in improved solution accuracy. A reÿned curvature model for VOF is also presented. With the newly developed interfacial treatments incorporated, both IB and VOF perform comparably well for the droplet dynamics under di erent ow parameters and uid properties.

Section: Introductionmentioning

confidence: 99%

Assessment of volume of fluid and immersed boundary methods for droplet computations

Lörstad

François

Shyy

et al. 2004

“…For example, in bubble and drop dynamics problems of an air-water system, the density ratio is about 1000. Many different flow methods [1,2] have been proposed to track the interface between two flows. For examples, they include the volume of fluid (VOF) [3], level set [4], immersed boundary (IB) [5], sharp interface technique [6], moving particle method [7], and lattice Boltzmann methods [8,9].…”

Section: Introductionmentioning

confidence: 99%

A pressure correction‐volume of fluid method for simulation of two‐phase flows

Lin

Chin

et al. 2010

SUMMARYA pressure correction method coupled with the volume of fluid (VOF) method is developed to simulate two-phase flows. A volume fraction function is introduced in the VOF method and is governed by an advection equation. A modified monotone upwind scheme for a conservation law (modified MUSCL) is used to solve the solution of the advection equation. To keep the initial sharpness of an interface, a slope modification scheme is introduced. The continuum surface tension (CST) model is used to calculate the surface tension force. Three schemes, central-upwind, Parker-Youngs, and mixed schemes, are introduced to compute the interface normal vector and the gradient of the volume fraction function. Moreover, a height function technique is applied to compute the local curvature of the interface. Several basic test problems are performed to check the order of accuracy of the present numerical schemes for computing the interface normal vector and the gradient of the volume fraction function. Three physical problems, two-dimensional broken dam problem, static drop, and spurious currents, and three-dimensional rising bubble, are performed to demonstrate the efficiency and accuracy of the pressure correction method.

“…The main approaches to simulate fluid flows in complex moving geometries use either moving-grid or artificial boundary methods [1][2][3][4][5][6]. This former type of methods imply re-meshing processes, which are highly expensive computationally in the fluid/elastic-structure interaction cases that involve large structure deformations.…”

Section: Introductionmentioning

confidence: 99%

On the Fourier representation of elastic immersed boundaries

Pacull¹,

Garbey

2009

SUMMARYThis paper presents an efficient treatment of fluid/elastic-structure interactions that takes advantage of the Fourier representation of immersed boundaries. We assume that the fluid is incompressible with uniform density and viscosity and that the immersed boundaries have fixed topologies. These elastic bodies can have large deformations and evolve anywhere within the fluid domain. They may be thick and are assumed to be piecewise smooth. We process the fluid-structure coupling with the immersed boundary method of C. S. Peskin. We can take advantage of the Fourier representation of the immersed bodies in many ways. First, the use of Fourier expansions allows us to filter out the high frequencies of the spatial oscillations along the boundary vectors. Second, we can work with a smaller number of boundary points to represent the interface, while preserving the same level of accuracy as long as enough points are used in the force spreading process. Finally, the harmonic information gathered by the Fourier coefficients is useful to control some global properties of the immersed boundaries. For example, we introduce a technique that corrects the volume conservation issue of closed immersed boundaries by performing constrained optimization in the Fourier space. We illustrate our method with two applications: one is a suspension flow with a large number of elastic 'bubbles', the other is an interesting case of artificial motion based on inertia rather than on flapping fins or flagella.