Radial Point Interpolation Method For Solving Two Dimension Heat Conduction Problems With Phase Change

In nature and engineering,many problems are closely related to the heat conduction with phase change.There is a gradually drifting interface between solid and liquid phases,where the release and absorption of phase change enthalpy at the phase change interface are occurred ceaselessly.So,it is a classical moving interface problem.Those traditional numerical methods based on mesh cannot track the moving interface accurately and conveniently.Radial point interpolation method(RPIM)is a novel meshless Galerkin method,which uses a series of random distributed nodes to discretize the problem domain and employs the radial basis function to construct the meshfree shape functions.In terms of Galerkin weak form,the resultant system equation of RPIM can be obtained easily.The RPIM was successfully applied to solving two-dimensional and three-dimensional solid mechanics,geometric nonlinear problems because of its advantages including the accuracy,simplicity and implementation of the essential boundary conditions easily.Addition,the model of the RPIM is very suitable to solve the special problems,such as mesh distortion and moving interface.The reason is that the RPIM is only based on nodes without any mesh information.So,the RPIM is used in this paper to analysis the heat conduction with phase change.In this paper,the development of numerical analysis of heat transfer with phase change and RPIM method are introduced.In section 2,we derived the shape function of the RPIM and collected its properties.To investigate the convergence and accuracy,the RPIM was developed to solve the steady state heat transfer problems in section 3.The system equation of RPIM is derived by using weighted residual method.The results of several numerical example show that the RPIM is convergent and accurate.In section 4,RPIM is proposed to solve the heat conduction problem with phase change by combination the sensible heat capacity method.The temperature field function is constructed by radial point Interpolation while and the system equation is discretized based on the weighted residual method.The feasibility and validity of the proposed method are verified by two classical Stefan examples.So it provides a new way for solving such problems.The results show that the proposed method is simple and easy to implement.Under the same conditions,the method has good consistency with analytical solutions and other algorithms,and can accurately calculate the phase transition interface.Based on this,it lays a foundation for the next research direction.