求解渗流自由面的逐步剖分法

发布时间：2019-04-23 07:33

【摘要】：渗流自由面的求解是渗流分析中的难题之一。渗流自由面是渗流场中的待求边界,需同时满足水头值等于高程(第一类边界条件)和流量交换为零(第二类边界条件)。在以往的研究工作中,采用虚单元法、初流量法等有限元法求解渗流自由面,为提高计算精度,通常通过提高迭代次数来逐步逼近第一类边界条件或第二类边界条件,计算复杂。本文提出了基于实域能量损失率最小求解稳定渗流场自由面的逐步剖分法,该方法物理意义明晰,计算精度高。主要研究成果包括:1、基于六节点三角形单元优化了渗流自由面。六节点三角形单元在以往的平面渗流自由面求解中是未曾被采用的。本文对平面渗流计算常用的三角形单元和等参四边形单元比较分析,六节点三角形单元具有如下优势:(1)能适应形状复杂的渗流边界;(2)能以完全二次多项式表达非线性水头插值函数。基于六节点三角形单元划分网格,应用优化的虚单元法求解了矩形渗流模型的渗流自由面,与电模拟试验解的比较表明,求得的渗流自由面精度更高,更接近其真实状态。2、基于实域能量损失率最小提出求解渗流自由面的逐步剖分法。对有确定上、下游边界以及自由渗出边界的渗流场,进行有限单元划分,由渗流溢出点逐步向渗流汇入点推进求解渗流自由面点,每推进一层单元,基于实域能量损失率最小求解该剖面上的自由面点位置,直到得到完整的渗流自由面以及完整的渗流实域。3、应用Fortran语言编写了逐步剖分法的计算程序,求解了有电模拟试验解的矩形坝、有模型试验解的矩形坝、有解析解的梯形坝的渗流自由面。逐步剖分法计算结果分别与电模试验解、甘油试验解和解析解对比,最大相对误差分别是4.94%、1.37%和2.57%。结果表明,逐步剖分法具有很高的计算精度。
[Abstract]:The solution of seepage free surface is one of the difficult problems in seepage analysis. The seepage free surface is the boundary to be solved in the seepage field, and the head value is equal to the elevation (the first type boundary condition) and the flow exchange is zero (the second type boundary condition) at the same time. In previous research work, the finite element method such as virtual element method and initial flow method was used to solve the seepage free surface. In order to improve the calculation accuracy, the boundary conditions of the first or the second kind are approximated gradually by increasing the number of iterations. The calculation is complicated. In this paper, a step-by-step method for solving the free surface of steady seepage field based on the minimum real-domain energy loss rate is presented. The physical meaning of this method is clear and the calculation accuracy is high. The main results are as follows: 1. The seepage free surface is optimized based on the six-node triangular element. The six-node triangular element has never been used in solving the free surface of plane seepage. In this paper, the triangle element and isoparametric quadrilateral element commonly used in plane seepage calculation are compared and analyzed. The six-node triangular element has the following advantages: (1) it can adapt to the seepage boundary with complex shape; (2) the nonlinear head interpolation function can be expressed by complete quadratic polynomials. Based on the mesh of six-node triangular element, the seepage free surface of the rectangular seepage model is solved by using the optimized virtual element method. Compared with the experimental solution of electrical simulation, the obtained seepage free surface is more accurate and closer to its real state. Based on the minimum real-domain energy loss rate, a step-by-step partition method is proposed to solve the seepage free surface. For the seepage flow field with definite upstream, downstream boundary and free exudation boundary, the finite element division is carried out, and the seepage free surface point is solved gradually from the seepage overflow point to the seepage flow convergence point, with each layer of element advancing. Based on the minimum real-domain energy loss rate, the point position of the free surface on the profile is solved, until the complete seepage free surface and the complete seepage real domain are obtained. 3. The program of the progressive partition method is programmed with Fortran language. The seepage free surface of rectangular dam with electric simulated test solution, rectangular dam with model test solution and trapezoidal dam with analytical solution is solved. The maximum relative errors are 4.94%, 1.37% and 2.57%, respectively, compared with the electrical model test solution, glycerin test solution and analytical solution. The results show that the step-by-step method has high accuracy.
【学位授予单位】：烟台大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TV139.1

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