非线性布西尼斯克方程的直线解法及渗透系数反演计算

Numerical solution of Boussinesq equation based on straight-line method and inverse calculation of permeability coefficient

本文提出了一种新的求解非线性Boussinesq方程正问题的数值方法。该方法利用有限差分方法把描述河渠间地下潜水非恒定流动的非线性偏微分方程转化为常微分方程,通过Runge Kutta法求解。以此为基础,利用函数逼近及算子识别摄动法建立了渗透系数反演的正则迭代法,并给出了计算实例。其结果表明该方法具有数值精度高、稳定性好等优点。

The nonlinear Boussinesq equation describing the unsteady flow of groundwater between rivers or ditches is transformed into ordinary differential equation by using finite differential method. Then the equation is solved by means of Runge-Kutta method. On this basis, the normalized iterative method for inverse calculation of permeability coefficient is established by using approximation function and perturbation method for operator identification. Calculation example shows that this method possesses the advantages of high accuracy and stability.