Fluid Phase Transition And Calculation Of Surface Tension By SPH

In the early stage of formation of planetary systems,nebular matter can be considered as fluid medium.Firstly,the gravitational accretion drives these arbitrarily distributed fluid medium to accumulate at the center of mass,forming a star and a disk shaped structure surrounding it and the disk structure is called pre-planetary disk.Secondly,planets formed in the pre-planetary disk through further gravitational accretion process,we hope to recur the formation of pre-planetary disk via fluid mechanics.The main equation of fluid mechanics is the Stokes equation,ordinary nu-merical method of fluid mechanics represents the Stokes equation on a mesh;However,there are several difficulties to perform fluid mechanics calculation in a mesh system regarding to our problem.At first,it is difficult to represent open boundary conditions for a fluid medium in a finite mesh,and a coordinate mesh can also hardly resolute sharp matter distributions,at which the differen-tiation will have bad accuracy.Further more,there may exist phase interfaces in the medium,this will make the system to become a multi-medium problem,the interaction between the interfaces are difficult to be considered in mesh sys-tem.For these reason,we employ the Smoothed Particle Hydrodynamics(SPH)method,this description can be easily resolved the following problems:a.Open boundary conditions;b.Discontinuous medium,that is,density or other physi-cal quantities showing a jumping change in the space;c.Medium phase change,and the interaction between different phases.This article is proceeded as follows,at first,we implemented the SPH method to solve Stokes equation.Then,we introduced our equation of state to describe the fluid medium,so that the model can describe the physical prop-erties of the fluid medium correctly.Finally,we applied our equation of state combined with the Stokes equation described by SPH and calculated the time evolution of the material without gravitational force.From the calculation re-sults,we find that a squarely initiated fluid medium forms a circular boundary due to the surface tension.This reflects the correct phase and evolution process.Therefore,our equation of state combined with hydrodynamics can correctly de-scribe the physical properties of fluid medium.In future works,we will include gravitation interactions to consider the dynamics of nebular materials.