| 对流扩散方程不同格式的数值稳定性分析 |
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| 引用本文： | 阴继翔,李国君,李卫华.对流扩散方程不同格式的数值稳定性分析[J].太原理工大学学报,2004,35(2):121-124,133. |
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| 作者姓名： | 阴继翔 李国君 李卫华 |
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| 作者单位： | 1. 西安交通大学,能源与动力工程学院,陕西,西安,710049;太原理工大学,电气与动力工程学院,山西,太原,030024
2. 西安交通大学,能源与动力工程学院,陕西,西安,710049 |
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| 基金项目： | 国家863计划重大专项资助项目(2002AA503020) |
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| 摘 要： | 利用数值计算方法对一维、线性、无源、两点边值问题的对流扩散方程在均分网格下不同格式的稳定性进行了分析，通过理论推导和实际计算，得出了上述条件下中心差分格式(CD)、QUICK格式和稳定性可控(SCSD)格式的P△cr数，并对稳定性可以保证的(SGSD)差分格式进行分析探讨，验证了数值稳定性是格式固有的属性。在此基础上，二维问题进行数值计算，以资为复杂的多维问题对流离散格式的稳定性分析提供依据。
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| 关 键 词： | 对流-扩散 离散格式 稳定性 Peclet数 传热学 |
| 文章编号： | 1007-9432(2004)02-0121-04 |
| 修稿时间： | 2003年11月6日 |
Analysis of the Convection Numerical Stability of Convection-Diffusion Equation |
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| YIN Ji-xiang,LI Guo-jun,LI Wei-hua.Analysis of the Convection Numerical Stability of Convection-Diffusion Equation[J].Journal of Taiyuan University of Technology,2004,35(2):121-124,133. |
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| Authors: | YIN Ji-xiang[ ] LI Guo-jun LI Wei-hua |
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| Institution: | YIN Ji-xiang~[1,2],LI Guo-jun~1,LI Wei-hua~1 |
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| Abstract: | The stability of one dimensional discretized convection diffusion equation is analyzed and summarized under first kind boundary condition,linear , source -free and uniform grid. The critical grid Peclet numbers for central difference scheme(CD),quick scheme and stability controllable second order difference scheme (SCSD) are obtained by inference of the theory and calculation of the practice based on the mentioned conditions. At the same time, stability guaranteed second order difference scheme (SGSD) is analyzed. It is demonstrated that stability is intrinsic attributes of the difference scheme. On the basis, the two dimensional convective diffusion equations are inquired for the same schemes mentioned above in order to provide the basis of analyzing the stability of multidimensional discretized convection scheme. |
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| Keywords: | convection diffusion discretized scheme stability Peclet number |
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