Modified equations for surface tension are derived by modifying normal and curvature with corrected smoothed particle method(CSPM).It is based on smoothed particle hydrodynamics(SPH) method with surface tension proposed by Morris.Both Morris and our method are tested via a semicircular problem.Factors that affect accuracy are investigated including surface definition,normal and curvature calculation.Smoothed length in curvature calculation is also confirmed reasonable.Furthermore,formation of a liquid drop with initial square shape under surface tension is simulated.Compared with Morris method and grid-based volume of fluid method,it is proved that the accuracy of our method is higher and particle distribution is more homogeneous.Finally,coalescence process of two oil drops in water under surface tension is simulated.

Control and synchronization of chaotic systems are studied.They are transformed into numerical optimization problems.A novel hybridization of differential evolution(DE) and bacterial foraging algorithm(BFOA),called CDEM algorithm,is proposed.The algorithm incorporates an adaptive chemotactic step from the BFOA into DE,which improves convergence of the classical DE.It introduces mutation operation of genetic algorithm for enhancing population diversity.Finally,CDEM algorithm is used to chaotic system control and synchronization.Numerical simulations based on Hénon Map demonstrate effectiveness and stability of the algorithm.Effects of parameters are investigated as well.

SPH (smoothed particle hydrodnamics) method with fully variable smoothing lengths is proposed. Different from existing adaptive kernel SPH methods, fully variable smoothing lengths are considered based on an adaptive symmetrical kernel estimation. An evolution equation of density is derived which implicitly couples with a variable smoothing length equation. Based on Springel' s fully conservative formulation SPH momentum equation and energy equation are derived by using symmetrical kernel estimation instead of scatter kernel estimation. An additional iteration process is employed to solve evolution equations of density and variable smoothing lengths equation. SPH momentum equation and energy equation are solved explicitly. Computation cost added by iteration is little. The equations and algorithm are tested via three ID shock-tube problems and a 2D Sedov problem. It is showed that conservation of momentum and energy is improved substantially and variable smoothing lengths effect is corrected, especially in the 2D Sedov problem. Pressure peak position and pressure at center are more accurate than those by Springel's scheme. The method deals with large density gradient and large smoothing length gradient problems well, such as large deformation and serious distortion problems in high velocity impact and blasting.

A solution of transpiration control equation is investigated in this paper. It is found that the equation can be classified as the classic heat transfer equation under certain conditions by means of variable alternation and then the analytic solution can be obtained. A numerical calculation of the analytic solution by a computer has proved the existence, uniqueness and stability of the solution. The theoretical problem of this sort of control system applied in the engneering is preliminarily ascertained. A finite difference numerical calculation has shown that the smaller the difference step is, the faster the difference solution approaches the analytic one. Because of limitation of the difference method, the steady numerical solution can be gotten in the region surrounded by R=0, BT=0 and R·BT=βτ/4h. The main conclusion of reference [2] is verified again.

In this paper the formulae of the collision probobilities for the isotro-pic two-dimensional neutron transport problem on the mixed region consisting of rectangular or triangle cells are given. Based on these formulae the code has been developed and applied to tow-dimensional mixed cells calculations. The calculated results show good agreement with those of Montecalo method and conservation principles.