| 用格子Boltzmann方法与拟小波方法研究二维扩散方程 |
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| 引用本文： | 阮航宇,李慧军.用格子Boltzmann方法与拟小波方法研究二维扩散方程[J].宁波大学学报(理工版),2006,19(2):222-227. |
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| 作者姓名： | 阮航宇 李慧军 |
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| 作者单位： | 宁波大学,理学院,浙江,宁波,315211 |
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| 摘 要： | 提出二维简单格子Boltzmann模型,并用其模拟扩散方程ut=uxx＋uyy,得到与精确解完全吻合的数值结果,成功地将格子Boltamann方法应用到二维偏微分方程的数值求解中;同时构造了二维问题的正则化样本尺度函数,在此基础上得到了二维问题的拟小波离散格式,并将其应用到扩散方程的数值求解中,得到与精确解拟合得非常好的数值结果.
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| 关 键 词： | 二维扩散方程 格子Boltzmann方程 多重尺度 拟小波方法 Runge-Kutta方法 |
| 文章编号： | 1001-5132(2006)02-0222-06 |
| 收稿时间： | 2005-09-06 |
| 修稿时间： | 2005年9月6日 |
Studies of Two-dimension Diffusion Equation Using Lattice Boltzmann and Quasi-wavelet Methods |
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| RUAN Hang-yu,LI Hui-jun.Studies of Two-dimension Diffusion Equation Using Lattice Boltzmann and Quasi-wavelet Methods[J].Journal of Ningbo University(Natural Science and Engineering Edition),2006,19(2):222-227. |
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| Authors: | RUAN Hang-yu LI Hui-jun |
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| Institution: | Faculty of Science, Ningbo University, Ningbo 315211, China |
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| Abstract: | In this paper,a simple Lattice Boltzmann model is proposed,and is used to simulate the diffusion equation(DE).The numerical results and exact solutions are almost completely fitting with each other.Based on this success,the lattice Boltzmann method is further extended to two-dimension(2-D) partial differential equation(PDE)and the results are fully satisfying.In addition,the regularization sampling scaling function of 2-D PDE equation is established,and based on which the quasi-wavelet discrete scheme is obtained.In the end,a simulation of the DE using the discrete scheme is performed,and the result shows the exact coincidence with the exact solution.ut= u xx + u yy |
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| Keywords: | two-dimension diffusion equation lattice Boltzmann equation multi-scale method quasi-wavelet method Runge-Kutta approach |
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