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求解非均质多孔介质中非饱和水流问题的质量集中有限体积法

发表时间:2011-11-15  浏览量:1455  下载量:711
全部作者: 贺新光,任理
作者单位: 湖南师范大学资源与环境科学学院;中国农业大学资源与环境学院
摘 要: 基于修正的皮卡迭代格式,提出一种有效求解非均质多孔介质中非饱和水流问题的质量集中有限体积法(lumped mass finite volume method,LMFVM)。该方法具有局部质量守恒性。同时,为克服传统迭代法在每一个时间步上迭代求解全离散格式时收敛速度慢的缺点,采用一种依赖于矩阵限制和延拓的多重网格加速技术,建立适用于非均质非饱和流动问题的有限体积离散格式的多重网格算法,从而大大加快了迭代收敛速度。为验证所提出LMFVM的有效性与精确性,对水力参数随机生成并呈对数正态分布的非饱和水流问题进行数值试验。计算结果表明:所提方法比仅具有全局质量守恒性的质量集中有限元方法(lumped mass finite element method, LMFEM)具有更高的计算精度和更低的全局质量平衡误差。
关 键 词: 水文学;非饱和水流;非均质多孔介质;理查德方程;有限体积法;质量集中
Title: A lumped mass finite volume method for solving the unsaturated flow problems in heterogeneous porous media
Author: HE Xinguang, REN Li
Organization: College of Resources and Environmental Science, Hunan Normal University; College of Resources and Environmental Sciences, China Agricultural University
Abstract: In this paper a lumped mass finite volume method (LMFVM) is presented for effectively solving the unsaturated flow problems in heterogeneous porous media based on the modified Picard iteration scheme. The method satisfies the local mass conservation property. At the same time, a multigrid algorithm with matrix-dependent prolongations and restrictions, which is adapted to the finite volume discrete scheme of the unsaturated flow problems in heterogeneous porous media, is constructed to overcome the difficulties when traditional relaxation methods are used to treat the fully discrete scheme at each time step, and a fast solution is obtained. Numerical experiments are carried out for the unsaturated flow equation with randomly generated lognormal hydraulic parameters to demonstrate the efficiency and accuracy of the developed method. The numerical results show that the LMFVM provides considerably higher level of accuracy and smaller error of global mass balance than does the lumped mass finite element method (LMFEM) only with the global mass conservation property.
Key words: hydrology; unsaturated water flow; heterogeneous porous media; Richards' equation; finite volume method; lumped mass
发表期数: 2011年11月第21期
引用格式: 贺新光,任理. 求解非均质多孔介质中非饱和水流问题的质量集中有限体积法[J]. 中国科技论文在线精品论文,2011,4(21):1985-1993.
 
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