| 改进的节块展开法求解对流扩散方程的稳定性和误差分析 |
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| 引用本文： | 邓志红,孙玉良,李富,Rizwan-uddin.改进的节块展开法求解对流扩散方程的稳定性和误差分析[J].原子能科学技术,2014,48(2):298-304. |
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| 作者姓名： | 邓志红 孙玉良 李富 Rizwan-uddin |
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| 作者单位： | 1.清华大学 核能与新能源技术研究院，北京100084；2.伊利诺伊大学 香槟分校，伊利诺伊州61801，美国 |
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| 基金项目： | 国家重大科技专项经费资助项目(ZX06901) |
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| 摘 要： | 对改进的节块展开法（MNEM）求解对流扩散方程进行了深入研究。利用符号不变原则理论上分析了MNEM的稳定性，分析结果显示，MNEM是一种具有固有稳定性的求解方法。通过数值实验对MNEM的计算误差进行了分析。数值结果表明：对于一维问题，MNEM至少具有3阶精度；对于多维问题，受横向泄漏近似的影响，MNEM表现为2阶精度。
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| 关 键 词： | 改进的节块展开法 对流扩散方程 稳定性 误差分析 |
Stability and Error Analysis on Modified Nodal Expansion Method for Transient Convection-diffusion Equation |
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| DENG Zhi-hong,SUN Yu-liang,LI Fu,Rizwan uddin.Stability and Error Analysis on Modified Nodal Expansion Method for Transient Convection-diffusion Equation[J].Atomic Energy Science and Technology,2014,48(2):298-304. |
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| Authors: | DENG Zhi-hong SUN Yu-liang LI Fu Rizwan uddin |
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| Affiliation: | 1.Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China;2.Nuclear, Plasma, Radiological Engineering, University of Illinois at Urbana Champaign, Urbana 61801, USA |
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| Abstract: | To further investigate the features of modified nodal expansion method (MNEM) for solving the convection-diffusion equation, the stability and error analysis were carried out. Based on sign preservation principle, the stability analysis reveals that the MNEM has inherent stability. The error analysis was implemented through a series of numerical experiments, and the results show that the MNEM is 3rd order scheme for one dimensional problem, while as 2nd order scheme for multi-dimensional problem because of using simple transverse leakage approximation. |
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| Keywords: | modified nodal expansion method convection-diffusion equation stability error analysis |
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