【摘要】 目前,采用"transmissivity"(导水系数)法将Boussinesq方程线性化后再求解是解决问题的主要手段,其中求解方法包括调和平均值法,几何平均值法和算术平均值法,为了对比它们的优劣性,结合水头线方程的性质(凹凸性)和平均值的性质,以均质各向同性的潜水稳定流Boussinesq方程为例,通过解析解,建立不同差分格式的误差方程,推导差分格式的收敛性条件,最后,通过数值实验检验不同差分格式的误差,结果表明:若网格步长(单元格长度)不趋于0,采用调和平均值建立的差分方程误差比较大,不能收敛到精确解;采用几何平均值时,误差较小,但是采用算术平均值时,差分方程是无条件收敛性的。更多还原

【Abstract】 The main method to solve Boussinesq equation is to linearize it by "transmissivity" firstly,which is calculated by three known average methods,such as harmonic mean,geometric mean and arithmetic mean.In order to contrast the errors caused by different average methods,combining the property of the function of hydraulic head(concave/convex) and the average methods,the error formula of varying finite difference schemes of Boussinesq equation is established to examine the convergent conditions,and compare the errors through the numerical experiments.The results show that control equation solved by the finite difference method in an isotropic and homogeneous aquifer,if the grid spacing does not approach zero,the finite difference scheme of Boussinesq equation whose thickness of the aquifer is calculated by the harmonic mean does not converge,while the convergence of the one calculated by the geometric mean is better.However,the one calculated by the arithmetic mean converges unconditionally.更多还原