基于有限体积法的三维稳态渗流计算方法及其应用

Three-dimensional steady seepage calculation method based on finite volume method and its application

为提升三维渗流数值计算的效率,提出了一种基于有限体积法的三维渗流计算模型。该模型采用无系数矩阵数值迭代求解方法对渗流控制方程进行离散,用预处理共轭梯度算法快速求解代数方程组,减少了内存占用;使用固定网格变渗透系数法求解计算域内含有浸润面的问题,应用OpenACC-GPU并行技术加速代数方程组的求解。采用二维均质坝渗流算例对模型进行了评估与验证,通过与GEO-Studio(2018学习版)软件的计算结果进行对比,发现两者计算结果误差在±2.5%以内,压力水头与总水头等值线的分布情况吻合,浸润线位置接近。证明所提出的渗流计算模型有效可行,并且通过并行技术提高了求解效率。进一步使用该渗流模型计算了一个三维面板堆石坝的工程实例,并将最大典型断面结果与GEO-Studio软件的计算结果进行了对比,结果表明该模型能够满足工程渗流计算的实际需要,可以在实际工程中应用。

In order to improve computing efficiency of 3D seepage calculation,a three-dimensional seepage calculation model based on finite volume method was proposed.The model used a coefficient-free matrix numerical iterative method to discretize the controlling equation and employed the precondition conjugate gradient algorithm to efficiently solve the algebraic equations,also it used fixed grid variable permeability coefficient method to solve the problem of containing seepage surface in the computational domain.We applied the OpenACC-GPU parallel technique to accelerate the solution progress.The model was evaluated and validated using a two-dimensional homogeneous dam seepage calculation.By comparing the results of proposed model and the results of GEO-Studio(2018 learning version)software,it was found that the errors of both calculation results were within 2.5%,the distributions of pressure water head and total water head contours matched with each other,and the position of seepage lines were close,which proved that the seepage calculation model proposed in this paper was effective and feasible,and the solution efficiency was accelerated.Finally,the seepage model was used to calculate a 3D concrete face rockfill dam,and the results of the maximum typical section were compared with those of GEO-Studio software,indicating that the model could meet the practical needs of engineering seepage calculation and could be applied in practical engineering.