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A boundary element method for calculating the shape and velocity of two-dimensional long bubble in stagnant and flowing liquid

机译：停滞和流动液体中二维长气泡的形状和速度的边界元方法

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A numerical method based on a boundary element method (BEM) has been developed for computing the velocity and the shape of long bubbles moving steadily in stagnant and flowing liquid in 2D case: plane and axisymmetrical. The flow is assumed to be inviscid and incompressible. The method consists in solving simultaneously a Poisson equation characterizing the flow and an equation for bubble shape in the form of a functional-differential equation resulting from both Bernoulli equation and the jump conditions at the interface. The Poisson equation is solved by a BEM with an iterative loop for nonlinear source term while the system of nonlinear algebraic equations obtained by discretizing the equation on the interface is solved by the Powell's hybrid algorithm. The bubble shape and velocity are obtained as a part of the solution. The problem of multiple solutions is investigated numerically and the maximum velocity criterion is used for selecting the physical solution. The results obtained by the simulation are in good agreement with the experimental and numerical results of previous studies. (C) 2006 Elsevier Ltd. All rights reserved.
机译：已经开发了一种基于边界元方法（BEM）的数值方法，用于计算在二维和二维情况下在停滞和流动的液体中稳定流动的长气泡的速度和形状。假定流动不粘稠且不可压缩。该方法在于同时求解由泊松方程和表征气泡的方程，以及由伯努利方程和界面处的跃变条件所产生的泛函方程形式的气泡形状方程。泊松方程由带有迭代回路的边界元法求解非线性源项，而通过在界面上离散方程组得到的非线性代数方程组由鲍威尔混合算法求解。气泡的形状和速度是溶液的一部分。数值研究了多重解的问题，并以最大速度准则来选择物理解。通过仿真获得的结果与先前研究的实验和数值结果非常吻合。 （C）2006 Elsevier Ltd.保留所有权利。

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