饱和－非饱和土壤渗流过程中Richards方程的分析与计算 Alternative Title The analysis and the computation for Richards' equation during the infiltration process in saturated and unsaturated soil 赵晨霞 Thesis Advisor 钟承奎 ; 周宇斌 2016-05-22 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 博士 Keyword Richards 方程 半解析解 冻土耦合模型 并行算法 保结构方法 Abstract Richards 方程是描述土壤渗流过程的基本控制方程. 本文主要在以下几个方面进行了相关工作:针对分层土壤下一类 Gardener-Basha 型 Richards 方程, 分析分层界面处本构关系,得到形式上的解析解,然后离散时间层,通过迭代的方式,得到方程半解析解,避免了分层界面处的数值震荡.对空间1维采用3次B样条基有限元,对空间2维采用5次Hermit 型插值有限元,保证了解u在\$\Omega\$ 上的整体光滑性,缓解非物理震荡现象.时间层用s级2s阶隐辛Runge-Kutta方法进行数值离散,以便在积分过程中长时间保持系统的固有特性.考虑了与 Richards 方程相关的一类冻土耦合模型--水热耦合模型,对耦合模型中的两个基本方程,分析并整理本构关系,给出基于差分方法的数值计算格式,在此基础上,完善模型方程,给出基于有限元方法的计算格式.本文对使用广泛的 Gauss 消去法,设计了一种列行调整双向流水线并行算法, 从通信时间、并行度、可扩展性方面分析该算法的性能, 并进行了数值实验. Other Abstract Richards' equation is the governing equation during the infiltration process in soil. For a class of Gardener-Basha Richards' equation describing layered soil, we give a method to get the semi-analytical solution. By analyzing the constitutive relation on the layered interface and discreting temporal dimension, we get the iterative scheme and get the semi-analytical solution. To meet the requirements of smoothness , Cubic spline basis EFM is used for one dimension and Hermit interpolation function with 5 order is used for two dimensions. Implicit symplectic Runge-Kutta method of s-stage and 2s-order is used to discrete temporal dimension. We give the calculating schemes for a kind of Coupling model of frozen soil. For getting the resolves of linear equations parallely, the method of column pivot with double loops is presented. This method is superior to the traditional row-partition and column-partition method in communication time, degree of parallelism and scalability. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225621 Collection 数学与统计学院 Recommended CitationGB/T 7714 赵晨霞. 饱和－非饱和土壤渗流过程中Richards方程的分析与计算[D]. 兰州. 兰州大学,2016.
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