Numerical simulations of three-dimensional foam by the immersed boundary method

Kim, Yongsam; Lai, Ming-Chih; Peskin, Charles S.; Seol, Yunchang

doi:10.1016/j.jcp.2014.03.016

Cited by 9 publications

(11 citation statements)

References 25 publications

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“…With Lagrangian methods, such as front-tracking [20], immersed-boundary [21], or arbitrary Lagrangian-Eulerian (ALE) [22] methods, the interface is represented explicitly by conforming discretization elements. Although these methods have been extended to multi-region systems [23,24,25,26,27,10], it is difficult to handle complex topological changes during interface-network evolution, especially in three dimensions. With Eulerian methods, such as volume-of-fluid (VOF) [28] and level-set methods [29], the interface is reconstructed from scalar fields, i.e., volume fraction or levelset field.…”

Section: Introductionmentioning

confidence: 99%

High-resolution method for evolving complex interface networks

Pan

Adams

2018

Computer Physics Communications

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In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local level sets and reconstruction of a global regional level sets, (ii) locally transporting the interface network by employing high-order spatial discretization schemes for improved representation of complex topologies. Various numerical test cases of multi-region flow problems, including triple-point advection, single vortex flow, mean curvature flow, normal driven flow and dry foam dynamics, show that the method is accurate and suitable for a wide range of complex interface-network evolutions. Its overall computational cost is comparable to the Semi-Lagrangian regional level-set method while the prediction accuracy is significantly improved. The approach thus offers a viable alternative to previous interface-network level-set method.

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Section: Introductionmentioning

confidence: 99%

High-resolution method for evolving complex interface networks

Pan

Adams

2018

Computer Physics Communications

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“…These works have also provided a solution to handle the topological changes during the interface moving in two-dimensional case in [18]. Recently, the IBM has been extended to three-dimensional cases in [14,19,43]. A summary of IBM and its applications can be found in [39].…”

Section: Introductionmentioning

confidence: 99%

A weak formulation for the multiphase Stokes flow problem without body fitting grids

Ying

Hou

Leung

et al. 2018

Pure and Applied Mathematics Quarterly

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We develop an effective interface tracking method to simulate the incompressible Stokes flow with moving interfaces. The Stokes equations are first rewritten into a system of elliptic equations with singular sources which can be efficiently solved by a simple weak formulation proposed in [11]. The key idea is to first split the solution into a singular part and a regular part additively. The singular part captures the interface conditions, while the regular part approximates the equations in the whole domain, which can be solved by the standard finite element formulation. We carefully design numerical methods to interpolate the velocity to the moving interface. Numerical tests are carried out to demonstrate the accuracy and other properties of our method.

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“…The Immersed Boundary (IB) method [34] is a general mathematical framework for the numerical solution of fluid - structure interaction problems arising in biological and engineering applications. The IB method was introduced to simulate flow patterns around the heart valves [32,33], and since its success in modeling cardiac fluid dynamics [31,15,16,14], it has been extended and applied to various other applications, including but not limited to motion of biological swimmers [3,30], dynamics of red-blood cells [9] and dry foam [21,22], and rigid body motion [20,43].…”

Section: Introductionmentioning

confidence: 99%

“…Their IB method with modified finite-difference operators (herein referred to as IBModified) was applied to a two-dimensional model of the heart, and it achieved improvement in volume conservation by one-to-two orders of magnitude compared to IBCollocated. Nevertheless, a major drawback of IBModified that limits its use in applications is its complex, non-standard finite-difference operators that uses coefficients derived from the regularized delta function (but see [21,22] for applications). To address the issue of spurious currents across immersed structure supporting extremely large pressure differences, Guy and Strychalski [39] developed a different extension of the IB method that uses non-uniform Fast Fourier Transform [8,12] (NUFFT) to generate “spectral” approximations to the delta function, which also has superior volume conservation.…”

Section: Introductionmentioning

confidence: 99%

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

Bao

Donev

Griffith

et al. 2017

Journal of Computational Physics

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The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least scriptC1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

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Numerical simulations of three-dimensional foam by the immersed boundary method

Cited by 9 publications

References 25 publications

High-resolution method for evolving complex interface networks

High-resolution method for evolving complex interface networks

A weak formulation for the multiphase Stokes flow problem without body fitting grids

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

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