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| 求解一维对流扩散方程的一种三层有限差分格式 |
| Three - level Finite Difference Technique for the One-dimensional Advection - diffusion Equation |
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| DOI：10.3969/j.issn.1671-5322.2009.01.006 |
| 中文关键词: 三层有限差分格式 对流扩散方程 稳定性 数值模拟 |
| 英文关键词: three-level finite difference technique advection-diffusion equation stability numerical differentiation |
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| 摘要点击次数: 4511 |
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| 中文摘要: |
| 通过指数变换将方程变形,消去方程中的"对流项",再利用反指数变换和待定系数法,构造了求解一维对流扩散方程的一种三层差分格式.采用Von Neumann方法分析了差分格式的稳定性,得到了格式稳定的充分必要条件. |
| 英文摘要: |
| Various numerical techniques will be developed and compared for solving one-dimensional advection-diffusion equation with constant coefficient.These techniques are based on the exponent transform.It allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes.The new method is more accurate and is more efficient than the conventional technique.The scheme is free of numerical diffusion.The results of a numerical experiment are presented,and the accuracy is dicussed and compared. |
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