The Adaptive Cross Approximation Accelerated
Boundary Element Method For Bubble Dynamics
Author(s)
Z. Fu & V. Popov
Abstract
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.
Keywords: bubble dynamics, boundary element method, adaptive cross
approximation.
1 Introduction
Among all the numerical techniques, the Boundary Element Method (BEM) has
been particularly favoured for study of bubble dynamics. Analysis of bubble
evolution involves a geometrical change of bubble surface and transition of the
bubble; hence it can be represented as a moving boundary problem. The use of
the BEM allows for discretization of the bubble surface only, which significantly
simplifies the re-meshing process and therefore has been widely employed by
many researchers for the solution of this problem (e.g. Blake et al. [1], Chahine
[2], and Khoo et al. [3]).
Keywords
bubble dynamics, boundary element method, adaptive cross
approximation.
Related Book
Other papers in this volume
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