| 渗碳数学模型差分算法的条件稳定性和有效性 |
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| 引用本文： | 雷声,黄已立,戈慈水,余波.渗碳数学模型差分算法的条件稳定性和有效性[J].合肥工业大学学报(自然科学版),2002,25(1):156-160. |
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| 作者姓名： | 雷声 黄已立 戈慈水 余波 |
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| 作者单位： | 1. 安徽建筑工业学院数理系,安徽,合肥,230022
2. 合肥永信电脑股份有限公司,安徽,合肥,230001 |
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| 摘 要： | 渗碳扩散方程的差分算法是条件稳定的 ,不是绝对稳定的 ,网格比和空间、时间步长及合适的初边值条件都影响差分算法的稳定性和有效性。网格比和时间、空间步长都有合理的选择范围 ,总误差在某个最优的时间、空间步长时达到最小。扩散方程实际上是一个变系数的偏微分方程 ,扩散系数是碳质量浓度的函数 ,扩散系数取值变化对最终的碳质量浓度计算结果影响较大 ,实际计算时应进行修正
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| 关 键 词： | 渗碳数学模型 差分算法 稳定性 有效性 扩散系数 |
| 文章编号： | 1003-5060(2002)01-0156-05 |
| 修稿时间： | 2001年7月20日 |
Conditional stability and efficiency of the finite differential method in the carburizing mathematical model |
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| LEI Sheng ,Huang Yi li ,GE Ci shui ,YU Bo.Conditional stability and efficiency of the finite differential method in the carburizing mathematical model[J].Journal of Hefei University of Technology(Natural Science),2002,25(1):156-160. |
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| Authors: | LEI Sheng Huang Yi li GE Ci shui YU Bo |
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| Institution: | LEI Sheng 1,Huang Yi li 1,GE Ci shui 1,YU Bo 2 |
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| Abstract: | The finite differential method is stable conditionally rather than absolutely. Its stability and efficiency are affected by the net rate, the step length of space and time, and suitable boundary conditions. Both the net rate and the step length of space and time have a reasonable select range, and the total errors become minimal at the optimized step dimension of space and time. The diffusion equation is a partial differential equation. The diffusion coefficient is the function of carbon concentration, and the changing of the diffusion coefficient has great influence on the final value of carbon concentration, so the coefficient needs to be adjusted in the calculating process. |
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| Keywords: | carburizing mathematical model finite differential method stability efficiency diffusion coefficient |
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