土壤水盐运移方程的有限点法研究

发布时间：2018-05-29 02:27

本文选题：土壤水盐运移方程 + 有限点法　；参考：《西安理工大学》2017年硕士论文

【摘要】：无网格法是在局部域上的节点处定义形函数,能够在计算区域任意增减节点,克服了有限元法在数值计算中对网格的依赖。本文提出的有限点法属于无网格法的一种,有限点法采用移动最小二乘方法构造形函数,用配点法离散控制方程。对于土壤水盐运移模型中的对流-弥散模型,有限元法、有限差分法在对流占优情况下容易产生震荡,而有限点法在离散控制方程之前首先给控制方程施加稳定项,并在梯度变化较大的区域采用自适应迎风格式,可以有效的避免数值震荡。本文主要的研究工作有如下几个方面:首先,介绍了有限点法的基本原理和处理方法,包括移动最小二乘形函数的构造,权函数和支持域尺寸大小的选取方法、施加稳定项原理、自适应迎风格式的应用条件以及对控制方程的离散原则。其次,针对线性的一维、二维土壤盐分运移方程,构造了有限点数值算法;针对非线性的一维、二维土壤水分运动方程,对计算过程中用到的显式格式和隐式格式的处理方法做了介绍,构造了有限点数值算法。最后,分别针对一维、二维土壤水分运动方程和土壤盐分运移方程进行了数值模拟,深入讨论了数值模拟结果与支持域大小、空间步长和时间步长之间的关系,并分析了收敛阶和计算时间,进而将数值模拟结果分别与有限元法、特征有限元和有限差分法进行比较,说明本文提出的有限点法是有效的。
[Abstract]:The meshless method defines the shape function at the nodes in the local domain. It can add or subtract nodes arbitrarily in the computational area and overcome the dependence of the finite element method on the mesh in the numerical calculation. The finite point method proposed in this paper belongs to the meshless method. The moving least square method is used to construct the shape function and the collocation method is used to discretize the governing equation. For the convection-dispersion model of soil water and salt transport model, the finite element method and the finite difference method are prone to oscillate in the case of convection, while the finite point method first applies a stable term to the governing equation before discretization of the governing equation. The adaptive upwind scheme is adopted in the regions with large gradient variation, which can effectively avoid numerical oscillation. The main research work of this paper is as follows: firstly, the basic principle and processing method of finite point method are introduced, including the construction of moving least square function, the selection of weight function and the size of support domain. The principle of stability, the application condition of adaptive upwind scheme and the principle of discretization of governing equations are given. Secondly, a finite point numerical algorithm is constructed for linear one-dimensional and two-dimensional soil salt transport equations, and for nonlinear one-dimensional and two-dimensional soil water motion equations, In this paper, the explicit and implicit schemes used in the calculation are introduced, and the finite point numerical algorithm is constructed. Finally, the one-dimensional and two-dimensional soil water motion equations and the soil salt transport equations are numerically simulated, and the relationship between the numerical simulation results and the size of the support domain, the space step and the time step is discussed. The convergence order and calculation time are analyzed, and the numerical simulation results are compared with the finite element method, the characteristic finite element method and the finite difference method, respectively. The results show that the finite point method proposed in this paper is effective.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：S153;O241.82

【参考文献】