瞬态空化泡演变过程的数值模拟

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。

Numerical Simulation on the Evolution of Transient Cavities

The interaction of three transient cavities and two cavities in the neighbourhood of a free surface are studied in the paper. The flow is supposed to be incompressible and potential. It is solved by using of the boundary integral equation and time stepping approach. In the numerical simulation the field boundaries are discreted by high order finite element representation and the singular integrals are calculated with special process. The numerical results show that the evolution of cavitation bubble appears in a number of vary different pattern when the calculation parameters (such as initial distance, radii et al) are changed, columnar jet, annular jet or both can take place in the collapse stage so that the cavitation bubble breaks up into a toroidal bubble or two small bubbles.