A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component. The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equation...A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component. The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equations. Then the Lie group method and the Runge-Kutta (RK) method were applied to the ordinary differential equations. The square conserving property and the accuracy of the two methods were compared. Numerical experiment results show the Lie group method has the good accuracy and the square conserving property than the RK method.展开更多
The chloride ion transmission model considering diffusion and convection was established respectively for different zones in concrete by analyzing chloride ion transmission mechanism under the dryingwetting cycles. Th...The chloride ion transmission model considering diffusion and convection was established respectively for different zones in concrete by analyzing chloride ion transmission mechanism under the dryingwetting cycles. The finite difference method was adopted to solve the model. The equation of chloride ion transmission model in the convection and diffusion zone of concrete was discreted by the group explicit scheme with right single point （GER method） and the equation in diffusion zone was discreted by FTCS difference scheme. According to relative humidity characteristics in concrete under drying-wetting cycles, the seepage velocity equation was formulated based on Kelvin Equation and Darcy＇s Law. The time-variant equations of chloride ion concentration of concrete surface and the boundary surface of the convection and diffusion zone were established. Based on the software MATLAB the numerical calculation was carried out by using the model and basic material parameters from the experiments. The calculation of chloride ion concentration distribution in concrete is in good agreement with the drying-wetting cycles experiments. It can be shown that the chloride ion transmission model and the seepage velocity equation are reasonable and practical. Studies have shown that the chloride ion transmission in concrete considering convection and diffusion under the drying-wetting cycles is the better correlation with the actual situation than that only considering the diffusion.展开更多
文摘A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component. The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equations. Then the Lie group method and the Runge-Kutta (RK) method were applied to the ordinary differential equations. The square conserving property and the accuracy of the two methods were compared. Numerical experiment results show the Lie group method has the good accuracy and the square conserving property than the RK method.
基金Funded by the National Natural Science Foundation of China(Nos.51278495,51174291)the Open Fund of Nation Engineering Laboratory for High Speed Railway Construction(No.HSR2013011)
文摘The chloride ion transmission model considering diffusion and convection was established respectively for different zones in concrete by analyzing chloride ion transmission mechanism under the dryingwetting cycles. The finite difference method was adopted to solve the model. The equation of chloride ion transmission model in the convection and diffusion zone of concrete was discreted by the group explicit scheme with right single point （GER method） and the equation in diffusion zone was discreted by FTCS difference scheme. According to relative humidity characteristics in concrete under drying-wetting cycles, the seepage velocity equation was formulated based on Kelvin Equation and Darcy＇s Law. The time-variant equations of chloride ion concentration of concrete surface and the boundary surface of the convection and diffusion zone were established. Based on the software MATLAB the numerical calculation was carried out by using the model and basic material parameters from the experiments. The calculation of chloride ion concentration distribution in concrete is in good agreement with the drying-wetting cycles experiments. It can be shown that the chloride ion transmission model and the seepage velocity equation are reasonable and practical. Studies have shown that the chloride ion transmission in concrete considering convection and diffusion under the drying-wetting cycles is the better correlation with the actual situation than that only considering the diffusion.
