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采用边界积分方程方法，对无粘流体中三个空化泡以及自由面附近二个空化泡相互作用的演变过程进行了数值模拟。计算中边界用二阶有限元离散，影响系数矩阵非对角线元素用六点高斯数值积分方法计算，对第一类、第二类完全椭圆积分用高次多项式近似，对计算系数矩阵对角线元素中遇到的奇异积分进行了特殊处理。结果表明，在不同的给定参数下，空化泡的溃灭形态各异，柱状射流和环形射流都有可能发生，使空化泡演变成双泡或环形泡。
The boundary integral equation method was used to simulate the evolution of the interaction of three cavitating bubbles and two cavitating bubbles in the vicinity of the free surface. In the calculation, the second-order finite element method is used to discretize the non-diagonal elements of the coefficient matrix. Six-point Gauss numerical integration method is used to calculate the first-order and second-order complete elliptic integrals. Singular integrals encountered in line elements are specially treated. The results show that under different given parameters, the collapsing state of cavitation bubbles are different, and the columnar and annular jets are likely to occur, and the cavitation bubbles evolve into double bubbles or annular bubbles.