A numerical simulation was performed to investigate two bubbles rising side by side in vertical channel using VOSET (Coupled Volume-of-Fluid and Level Set) method and N-S equations coupled with continuous surface force (CSF) model. Behaviors of coalescence between two identical bubbles predicted were in good agreement with experimental results reported in literature. Effects of surface tension on trajectories and velocities during rising process are investigated. Three types of motion were observed depending on surface tension:Coalescence, two bubbles repeatedly attracted and bounced against each other, bounced and separated. Without coalescence, trajectory shows symmetry about channel center line. Vertical velocities of both bubbles are almost the same while magnitude of horizontal velocity with opposite direction equals.

A single-component multiphase lattice Boltzmann model which combines effective mass function with special potential in calculating interparticle potential based on Shan-Chen model is proposed.Accuracy of the model is verified by simulating single-component phase change process.Different equations of state are explored in the model.It shows that the model has many advantages: It tallies with the Maxwell construction more precisely;The maximum magnitude of spurious current is smaller and the range of simulation temperature is greater.Laplace tests is carried out and simulated results are in conformity.

It reports the investigation on calculation methods of ground-state correlation energy of double-electron system atoms (or ions) by using B-splines basic sets. These methods belong to the application category of calculus of variations, and adopt B-splines techniques to account for the radial bases, and at the same time, deal with the angular bases by using Goldman's mixed L method. The calculation results are given for He, H^-,Li⁺,Be⁺⁺,B⁺⁺⁺ atoms (or ions) and compared with those of others' theoratical methods. This comparison demonstrates that our calculation methods have excellent computing accuracy and efficiency.