| 半无限区域上常系数对流扩散方程的解析解 |
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| 引用本文： | 冯安住. 半无限区域上常系数对流扩散方程的解析解[J]. 邵阳学院学报(自然科学版), 2012, 9(1): 19-22 |
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| 作者姓名： | 冯安住 |
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| 作者单位： | 长沙理工大学数学与计算科学学院,湖南长沙,410076 |
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| 基金项目： | 国家自然科学基金资助（10926189 10871031）; 湖南省自然科学衡阳联合基金资助（10JJ8008）; 湖南省教育厅重点项目资助（10A015） |
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| 摘 要： | 主要在半无限区域内研究均匀介质、稳定流条件下的二维对流扩散方程的解析解,针对常系数下两个问题：采用Laplace变换和Fourier变换相结合,求得连续一致输入浓度的下对流扩散方程的解析解;变坐标变换和Laplace变换,求输入连续增长性质下对流扩散方程的解析解.在得出相应的解析解后,与已有的解析解进行和数值解进行比较.
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| 关 键 词： | Laplace变换 Fourier变换 卷积 解析解 对流扩散方程 |
An Analytical Solution to Constant Coefficients Advection-diffusion Equation in the Semi-infinite Domain |
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| FENG An-zhu. An Analytical Solution to Constant Coefficients Advection-diffusion Equation in the Semi-infinite Domain[J]. Journal of Shaoyang University(Natural Science Edition), 2012, 9(1): 19-22 |
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| Authors: | FENG An-zhu |
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| Affiliation: | FENG An-zhu(College of Mathematics and Computing Science,Changsha University of Science and Technology,Changsha,Hunan 410076,China) |
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| Abstract: | This paper discusses the two-dimension advection-diffusion equation in a homogeneous and steady flow in the semi-infinite domain,and discusses the following two problems under the conditions of constant coefficients and variable coefficients respectively：,solution to continuous input concentration of uniform nature with the Laplace transform and Fourier transform,solution to continuous input concentration of increasing nature with moving coordinate system and Laplace transform.After these,we compare the analytical solutions with the published result in analytical solutions and numerical solutions. |
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| Keywords: | Laplace transforms Fourier transforms convolution analytical solutions advection-diffusion equation |
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