对流-弥散方程的小噪声方法与应用

Minor Noise Method and Application of Convection-dispersion Equations

通过小噪声摄动理论,建立了小噪声随机微分方程.并借助于摄动矩的理论,求出了随机微分方程质点位移的均值与方差,之后将对流-弥散方程进行正态近似,得到了方程的近似解.最后将小噪声摄动理论应用到求解实际的高对流-弥散方程中,并与广义差分迎风格式的方法作比较,得到了满意结果.

Random differential equations of minor noise were established by means of perturbation theory of minor noise. And using perturbation moment theory, the means and variances of random differential equations for material point shift were gotten. At last, the convection-dispersion equations were approximately normalized and the approximate solutions of the equations were gotten. Also the perturbation theory of minor noise was used for solving high convection-dispersion equations and the calculated results were compared with those gotten by generality difference format.