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在利用初流量法分析带有自由面的渗流问题时,常因采用高斯积分点作为结点初流量计算判断依据所带来的误差而令解出现振荡。为了减低这一因素的影响及提高计算的效率,针对常用的4结点平面单元和8结点6平面三维单元的自由面方程进行分析,提出采用坐标变换和等参变换等技术来改造结点初流量的计算,并建议按自由面穿越单元之状况引用分部积分,使其积分上、下限符合高斯积分法的格式化要求,从而可利用高斯积分法求出精确的结点初流量,而精确的结点初流量则有助于改善解的振荡及提高计算结果的精度。通过一矩形均质坝实例分析,表明该方法的稳定性和收敛性良好。
When using the initial flow method to analyze the seepage problem with free surface, the oscillation is often solved by using the Gaussian integral point as the initial flow of the node to calculate the error caused by the judgment basis. In order to reduce the influence of this factor and improve the computational efficiency, this paper analyzes the free-surface equations of the commonly used 4-node planar element and 8-node 6-plane 3D element, and proposes to transform the nodes by using the techniques of coordinate transformation and isoparametric transformation The calculation of the initial flow rate and the suggestion of referring to the fractional integral by the condition of the free surface crossing unit make the upper and lower integrals meet the requirements of the Gaussian integration method so that the accurate initial flow of the junction can be obtained by Gaussian integration method. The accurate initial flow of nodes helps to improve the solution oscillation and improve the accuracy of the calculation results. An example of a rectangular homogeneous dam shows that the stability and convergence of this method are good.