Numerical simulation of the bubble dynamics in a Hele-Shaw cell. 1

A. O. Tsebers

Institute of Physics, Latvian University Salaspils-1, LV-2169, Latvia

Abstract
A numerical algorithm is presented for simulating two-dimensional problems dealing with liquids with a free surface. The algorithm is based on an accurate calculation of Cauchy-type integrals along circular arc - shaped contour elements. Results of simulating the rising of small bubbles in vertical Hele-Shaw cells are presented. They illustrate the instability of the bubble front with respect to symmetric and asymmetric perturbations at small capillary numbers.