A fast algorithm for modeling multiple bubbles dynamics

Thanh, Tung Bui; Ong, Ee Ping; Khoo, Boo Cheong; Klaseboer, Evert; Hung, K. C.

doi:10.1016/j.jcp.2005.12.009

Cited by 38 publications

(27 citation statements)

References 30 publications

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“…Ever since, the method was used by many authors for a wide variety of problems using different expansion strategies. Bui et al [4] combined FMM with the Fourier transform to study multiple bubbles dynamics. Gumerov and Duraiswani [8] applied the FMM for the biharmonic equation in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Wavelet compression of parabolic diffusion integral kernels

Ravnik¹,

Škerget²

2014

WIT Transactions on Modelling and Simulation

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In this paper we examine the properties of steady and unsteady diffusion fundamental solutions in the framework of fast BEM. The fundamental solutions and their kernels form integral kernels in boundary integral equations. The properties of these kernels define the relationship between CPU time and storage gain versus the accuracy of sparse approximations in fast BEM.We show that, when solving a diffusion type problem, using unsteady fundamental solutions is advantageous over steady fundamental solutions. We examine the behaviour of fundamental solutions to show why the unsteady fundamental solution is better for fast BEM. Furthermore, we confirm the theoretical findings by simulation of viscous fluid flow and heat transfer. We consider steady cases, where a false transient approach is used so unsteady diffusion fundamental solutions may be employed. Finally, we examine cases of increasing non-linearity, to highlight that these findings apply to strongly nonlinear problems as well.

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Section: Introductionmentioning

confidence: 99%

Wavelet compression of parabolic diffusion integral kernels

Ravnik¹,

Škerget²

2014

WIT Transactions on Modelling and Simulation

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“…The Fast Fourier Transform (FFT) is applied to approximate the convolutions. The FFTM method has been successfully applied by Bui et al [6] for modelling multiple bubble dynamics, with clustering to fit in with the property of sparseness of the physical problem. It proves computationally effective and requires storage of O(N) (N is the degree of freedom).…”

Section: Introductionmentioning

confidence: 99%

The adaptive cross approximation accelerated boundary element method for bubble dynamics

Fu¹,

Popov

2012

WIT Transactions on Modelling and Simulation

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A model based on the adaptive cross approximation (ACA) accelerated boundary element method (BEM) is presented for solving bubble dynamics problems. The computational solution of multiple bubble dynamics problems has high CPU requirements since it involves moving gas-liquid phase interfaces. In order to efficiently solve such problems, a fast algorithm, i.e. adaptive cross approximation, is implemented to compress the induced collocation matrix. An efficient binary-bit key system is applied to build up a hierarchical tree structure for the discretized boundary. With the aid of the key system, the dense matrix is partitioned into blocks which satisfy the condition of admissibility or contain only one row/column. The implemented ACA-BEM numerical technique is verified using the Rayleigh-Plesset equation and it is shown to be of linear complexity.

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“…In the presence of multi-bubbles inside a fluid, homogenization is often applied. Bui [20] combined the fast Fourier transform on multipoles method and boundary element method to study the dynamics of multiple bubbles in moving boundary problems. Chen [21] used a front-tracking method to investigate the dynamic response of bubble cluster to pulses of pressure perturbation.…”

Section: Introductionmentioning

confidence: 99%

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

Sun

Zong

et al. 2011

Acta Mech Sin

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The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demonstrated in our calculation results.

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A fast algorithm for modeling multiple bubbles dynamics

Cited by 38 publications

References 30 publications

Wavelet compression of parabolic diffusion integral kernels

Wavelet compression of parabolic diffusion integral kernels

The adaptive cross approximation accelerated boundary element method for bubble dynamics

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

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