中国物理B ›› 2005, Vol. 14 ›› Issue (1): 21-27.doi: 10.1088/1009-1963/14/1/005

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Influence of stochastic disturbances on the quasi-wavelet solution of the convection-diffusion equation

董文杰1, 李建平2, 何文平3, 封国林4   

  1. (1)Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China; (2)Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;National Climate Center of China, Beijing 100081, China; (3)Department of Physics, Yangzhou University, Yangzhou 225009, China; (4)Department of Physics, Yangzhou University, Yangzhou 225009, China; Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • 收稿日期:2004-05-20 修回日期:2004-08-11 出版日期:2005-01-20 发布日期:2005-01-20
  • 基金资助:
    Project supported by the Key Innovation Project of the Chinese Academy of Sciences (ZKCX2-SW-210) and the National Natural Science Foundation of China (Grant Nos 40325015, 40035010 and 40275031).

Influence of stochastic disturbances on the quasi-wavelet solution of the convection-diffusion equation

He Wen-Ping (何文平)a, Feng Guo-Lin (封国林)ab, Dong Wen-Jie (董文杰)bc, Li Jian-Ping (李建平)b   

  1. a Department of Physics, Yangzhou University, Yangzhou 225009, China; b Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China; c National Climate Center of China, Beijing 100081, China
  • Received:2004-05-20 Revised:2004-08-11 Online:2005-01-20 Published:2005-01-20
  • Supported by:
    Project supported by the Key Innovation Project of the Chinese Academy of Sciences (ZKCX2-SW-210) and the National Natural Science Foundation of China (Grant Nos 40325015, 40035010 and 40275031).

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摘要： A quasi-wavelet numerical method (QWNM) is introduced for solving the convection--diffusion equation (CDE). The results manifest that the calculated bandwidth has an extremum. When the bandwidth takes the value of the extremum, the accuracy of the solution for the CDE by using the QWNM is relatively high, and better than that by using the up-wind scheme. Under the condition of stochastic boundary disturbances of different amplitudes, the results of the QWNM are a little worse than those of the up-wind scheme when the integral time is longer. However, when stochastic boundary disturbances of equal amplitudes occur, the solutions of the equation by using the QWNM and the up-wind scheme can be identical if the bandwidth takes an integer greater than or equal to 20. When the parameter is stochastically disturbed, the root-mean-square error of the quasi-wavelet solution of the equation is smaller than that of the up-wind scheme solution if the bandwidth is 10. When the initial values are stochastically disturbed and the bandwidth equals 10, the accuracy of the quasi-wavelet solution is relatively high, and better than that of the up-wind scheme solution.

关键词: stochastic disturbance, convection--diffusion equation, quasi-wavelet, up-wind scheme

Abstract: A quasi-wavelet numerical method (QWNM) is introduced for solving the convection--diffusion equation (CDE). The results manifest that the calculated bandwidth has an extremum. When the bandwidth takes the value of the extremum, the accuracy of the solution for the CDE by using the QWNM is relatively high, and better than that by using the up-wind scheme. Under the condition of stochastic boundary disturbances of different amplitudes, the results of the QWNM are a little worse than those of the up-wind scheme when the integral time is longer. However, when stochastic boundary disturbances of equal amplitudes occur, the solutions of the equation by using the QWNM and the up-wind scheme can be identical if the bandwidth takes an integer greater than or equal to 20. When the parameter is stochastically disturbed, the root-mean-square error of the quasi-wavelet solution of the equation is smaller than that of the up-wind scheme solution if the bandwidth is 10. When the initial values are stochastically disturbed and the bandwidth equals 10, the accuracy of the quasi-wavelet solution is relatively high, and better than that of the up-wind scheme solution.

Key words: stochastic disturbance, convection--diffusion equation, quasi-wavelet, up-wind scheme

中图分类号: 

  • 0340G