| 解对流-扩散方程的时空守恒元与解元法 |
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| 引用本文： | 岳月梅,李小春.解对流-扩散方程的时空守恒元与解元法[J].南京工程学院学报(自然科学版),2009,7(3):8-13. |
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| 作者姓名： | 岳月梅 李小春 |
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| 作者单位： | 1. 长沙理工大学数学与计算科学学院,湖南,长沙,410076
2. 湖南农业大学东方科技学院,湖南,长沙,410128 |
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| 摘 要： | 针对一维对流-扩散方程提出了时空守恒元与解元（CE／SE）法．α-μ格式将物理相关变量和它们的空间导数看成是独立的变量，非粘性α-μ格式是中性稳定的，即没有数值损耗，而它修改的α—ε格式，可通过ε来控制数值损耗．当数值解出现间断，α-ε格式并不能防止间断附近的摆动，而α-ε—α-β格式能有效地弥补这些不足．
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| 关 键 词： | 守恒元，解元 α-μ格式 α-ε格式 α-ε-α-β格式 |
Method of Space-time Conservation Element and Solution Element for Solving Convection-diffusion Equation |
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| YUE Yue-mei,LI Xiao-chun.Method of Space-time Conservation Element and Solution Element for Solving Convection-diffusion Equation[J].Journal of Nanjing Institute of Technology :Natural Science Edition,2009,7(3):8-13. |
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| Authors: | YUE Yue-mei LI Xiao-chun |
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| Institution: | 1. School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 4 10114, China; 2. Oriental Science ＆ Techology College, Hunan Agricultural University, Changsha 410128, China) |
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| Abstract: | A new method, the space-time conservation element and solution element （CE/SE） method for solving one-dimension convection diffusion equation is introduced. In α-μ scheme, the physical variables and their spatial derivatives are treated as independent variables. The inviscid α-μ. scheme is neutrally stable, that is, free from numerical dissipation, while the modified α -ε scheme controls numerical dissipation via ε. When discontinuities are present in a numerical solution, the α -ε scheme fails to suppress numerical wiggles that generally take place near these discontinuities, whereas the α-ε-α-β scheme is able to address this issue. |
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| Keywords: | conservation element solution element α-μ scheme α -ε scheme α-ε-α-β scheme |
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