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A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.

The author provides a new discretization method-the finite volume method(FVM). For the Stokes equation the velocity space is approximated by the nonconforming linear element based on the dual partition and the pressure by the piecewise constant based on the primal triangulation. Under the suitable smoothness of the solution, the optimal convergence rateO(h) is obtained, whereh denotes the parameter of the space discretization.

A continuous method is presented to deal with the discontinuous physical properties on both sides of solid/liquid interface during the solidification process. Then single dendrite evolution in two and three dimensions is simulated by using this method. Multi-grain evolution is also simulated during solidification by the method. The method is easy to be understood and does not need all details of dendrite. The simulated results can reflect the random characteristic of dendrite evolution and the micro-segregation of solute.

Research on the droplet impact on a hydrophobic surface is of important theoretical significance and engineering value, both in mesoscopic fluid mechanics and interactions between microfluid and special materials. The van der Waals (vdW) equation of state relates the pressure to the temperature and the density of the fluid, and gives the long-range attractive force and short-range repulsive force between particles. The van der Waals equation of state can be used to describe the surface tension between liquid and vapor. As a pure meshless particle method, the smoothed particle hydrodynamic (SPH) method can use the vdW equation of state written in SPH form of N-S equations to describe the surface tension. The vdW surface tension mode is validated by simulating the coalescence of two equally sized static droplets in vacuum. Repellant of the hydrophobic surface is derived from a core potential. By combining the vdW surface tension and the repulsive force of the surface, the phenomenon of a liquid droplet impact with a certain initial velocity on the hydrophobic surface is studied. The SPH model is not only capable to describe the spreading of the droplet after it contacts the surface, but also clearly reproduces the springback, bouncing and secondary impact of the droplet. During the deformation of the droplet, the inertia force impels the spreading process of the droplet whilst the springback and bouncing behavior is dominated by the surface tension. The simulated results are in good agreement with the published experimental observations and VOF simulated results, indicating that the way we treat the surface tension and the repulsive force of the hydrophobic surface is effective and applicable in droplet impact surface problems. The impact velocity and liquid viscosity are considered to be two important factors that affect the deformation of the droplet after it contacts the surface. By varying the impact velocity within a certain range it is concluded that the maximum liquid-solid contact area increases as the impact velocity grows, and the bounced droplet will leave the surface when the velocity is big enough. Another comparison between different liquid viscosities shows that the maximum contact area decreases as the liquid viscosity increases because of the viscous dissipation, and the droplet barely rebound when the liquid viscosity is big enough.

To investigate the process of droplet impact on an orifice plate, a two-dimensional SPH model is established. An improved linked-list search algorithm with improvement of computational domain changing with fluid is described. By analyzing the numerical results with the experimental data, influences of viscosity, gravity, and internal pressure on the spreading of droplet over the orifice are studied. It is demonstrated that spreading will change to jet flow after the droplet reaches the orifice, and then the jet will pass it rapidly and in this rather short time the effect of gravity contributes very litte to the motion. However, viscosity can induce the jet to move in a curve into the orifice. Besides, with the internal pressure and inertial effect, the lower part of the jet will fluctuate regularly. The fluctuations make the jet repeat inflation and absorption to absorb the fluid from higher pressure area, resulting in Hole Suction phenomenon. Through analyzing the pressure of the vertical section of orifice edge, we find that internal pressure plays a significant role to the droplet which is absorbed into the orifice and finally leads to splashing. Numerical results are in good agreement with the experimental data.

Highly reproducible KAr dating results of ∼4.5·105 a on a Chinese basalt sample with low K content and comparatively low atmospheric Ar suggest suitability as a Quaternary age standard. Interlaboratory standardisation in this young age range is a requirement for both archaeologists and geologists and is fundamental to geothermal and Pleistocene mineral deposit exploration.