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本文用向前差分法导出了通用的一维瞬态非线性扩散方程的差分方程;以此为基础编制的计算机程序得到了国际著名温度场非线性有限元程序ADINAT的检验。所编制的程序可适用于平面、柱面和球面等形状工件的渗碳过程控制或模拟,以及工件淬火冷却过程中的温度场分析等问题。其中的第Ⅱ类边界条件提供目前尚未解决的辉光离子渗碳和真空渗碳工艺中的工件碳分布控制的理论基础。
In this paper, we derive the difference equation of one-dimensional transient nonlinear diffusion equation by the forward difference method. The computer program based on this is tested by ADINAT, a non-linear finite element program of world famous temperature field. The programmed program can be applied to control or simulate the carburizing process of flat, cylindrical and spherical workpieces, as well as the analysis of the temperature field during quenching and cooling of workpieces. The Type II boundary conditions provide the theoretical basis for controlling the carbon distribution in the workpiece in the glow-ion carburizing and vacuum carburizing processes that have not yet been solved.