By direct numerical simulation of Navier-Stokes equations the reconnection of two anti-parallel vortex tubes has been studied in terms of the pseudo-spectral method.The influence of different disturbances for initial vortex tubes on reconnection is observed. "Curved vortex belts" are found,and the physical mechanism for the amplification of background vorticity is also investigated.

The design of open boundary condition (OBC) is one of the most challenging problems in the field of nummerical computation for N. S. equation. In this article the perturbation solution of N.S. equation in the region approaching to infinity is taken as the basis for designing the OBC. A testing example proposed by M.philip has been calculated. The results show that the present OBC is superior to all others existing in literature.

The motion of the film separating two fluid phases is studied when it begin to be attracted into a thin pipe. Finite element method, especially the similar element is used. The elements attaching to the film are changed step by step in the calculation. The computed entrancing length variation is consistent with experiments. The computation offers the whole detail of the now.

The Marker-and-Cell technique is modified and generalized to the flow problems of non-Newtonian fluid, especially of viscoelastic fluid. The solution can be obtained for reasonably high elastic Deborah number. Discussions are also on the bubble formation and growth at the orifice submerged under the Maxwell liquid in finite extent, which is a typical problem incorporating varieties of complexity, including the non-sphericity of the bubble, the viscoelasticity of the liquid and the complex flow field.

Two-dimensional imcompressible viscous flows around a circular cylinder with periodic oncoming flow from infinity are investegated. By means of spectrum method, the stream functions are developed into Fourier series, so the stream functions depend on angle 0 continuousely. Numerical calculations are implemented for stream functions as well as vortices for the case K_c=4 and Re=200. The results manifeste that the method used here has the advantage of simplicity and saving computer time comparing with the method of fully discretiged N-S egs. and discretiged vortices method.

Using BEM to solve vibrating or unsteady Stokes flow is very attractive. At first we derive the Green functions for 2D and 3D. Then we deduce the relative formula, the explicit expression for pressure and the boundary integral equation. The integral equation is discretized into a set of linear algebric equations. In the case of 2D, the influence coefficients of the segment to itself are integrated analytically. In order to check such BEM, an example with analytical solution already exists is solved numerically. The result shows that the method based upon our Green functions is perfect.

A hybrid method [1] is used to solve the wave of 3-D low Reynolds flow in an elastc pipe. The flow region is divided into far field and near fielf. In far field the solutions can be expressed by series expansions[2], while in the near field FEM could be used. 3-D eigen-functions must be taken into account. The corresponding eigen values are calculated numerically. It is shown that except the fundamental eigen functions which are just the 2-D ones, the others decrease very quickly. So 2-D eigen functions are enough for many cases.