A stable and efficient element-free Galerkin method is proposed for steady convection-diffusion problems.In the method integrations are computed with a local Taylor expansion nodal integral technique.According to convection-dominated degree,integration nodes are adaptively shifted opposite to the streamline direction.Compared with conventional element-free Galerkin method with stabilization,the method exhibits better stability and higher efficiency in solving convection-dominated convection-diffusion problems.It is a pure meshfree method,which is independent of background integral.Moreover,the method is easy to be implemented.

A corrected smoothed particle hydrodynamics(SPH) method is proposed,in which standard SPH method is corrected with a density re-initialization method.A treatment for solid wall boundaries is presented to improve numerical accuracy.Drop stretching and dam-breaking are simulated numerically to show validity and reliability of the method.Filling process in a channel is investigated,and effect of Reynolds number on flow field and vortex are analyzed.It shows that the corrected SPH method can simulate filling process in a channel precisely and the flow is affected significantly by Reynolds number.

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.