Numerical Simulation Of Phase Field Model Under Fourier Spectral Method

As an effective method for simulating the microstructure change of pure metals during solidification,the phase field method has always attracted the attention of researchers at home and abroad.The finite difference method,as the most general and common method,has always been the method of calculating discrete and solving phase field.However,the finite difference method has the disadvantages of large amount of computation,long operation time and low precision.In this paper,the discrete phase field model is solved by Fourier spectral method,and the phase field equation and temperature field control equation are solved by Fourier spectral method.Compared with the ordinary difference method of discrete phase field equation,the calculation steps are simplified and the accuracy is improved.The main tasks of this paper are as follows.Firstly,the phase field model proposed by the construction principle of pure metal phase field model is selected.This model consists of two partial differential equations,the phase field equation and temperature control equation,respectively.In combination with the effect of temperature,anisotropy,random disturbance and forced convection on the crystal morphology during the actual dendrite growth process,parameters such as physical parameters,anisotropic strength and thermal perturbation terms of a given metal material are added to the model,and coupled to the flow field,which can simulate crystal morphology in both static and dynamic cases.Secondly,the Fourier spectral method is used to solve the phase field model.The phase field equation and temperature field control equation are discretized by Fourier spectral transformation,which greatly reduces the process of solving the phase-field equation.The phase field method is used to simulate the crystallization process of pure metal crystal growth by Matlab process programming,and the crystallization program is visualized by Paraview software.In the end,the phase field model solved by Fourier spectral method reproduces the dendrite,lamella and polycrystalline core morphology of pure metal crystallization.In order to prove the validity of the phase field model using the Fourier spectral method in simulating pure metal crystallization,the influence of each model parameters on crystal morphology was studied under static and dynamic conditions.The effects of anisotropy,equilibrium temperature,interface thickness,latent heat and interfacial noise on crystal growth morphology under static condition and flow velocity,interfacial noise on crystal growth morphology under dynamic condition are studied quantitatively by simulation comparison.Finally,properly increasing the value of the equilibrium temperature can promote the crystal growth.Increasing the value of interface thickness can accelerate the crystal growth of metal crystals.When the latent heat increases,the number of lateral branches increases and the lateral branches become thinner.Thermal disturbances have important effects on dendrite morphology,interface structure and lateral branches.The flow velocity affects the dendrite growth in the upstream and downstream directions.