


各向异性渗流模拟的延迟修正方法
漆力健 廖华胜 李连侠
各向异性渗流模拟的延迟修正方法
The Deferred Correction Method in Numerical Simulation of Anisotropic Seepage Flow
各向异性渗流渗流的数值计算时,当主渗透方向与坐标轴交叉时,系数矩阵的对角不占优往往使计算难以进行。本文从各向异性渗流控制方程本身出发,将由于主渗透方向与坐标轴不一致而产生的、易导致矩阵对角不占优的交叉项移至源汇项中,采用延迟迭代方法逐步逼近原方程的解,增强计算的稳定性,同时提高了求解结果的精度,较好的解决了带有交叉项的各向异性渗流数值求解问题。
In seepage flow simulation, the directions of principal permeation are not always coincided with the axises of global computational coordinates because of complex geologic structure of the natural porous medium. When the traditional method is applied, it can result in an illness discreted coefficient matrix and incorrect solution as a result of the fact that it is not a diagonal-dominance matrix. On the basis of anisotropic governing equation, a new method to divide the permeability tensor into two parts, diagonal elements and non-diagonal ones, then a differed correction method was employed to approach anisotropic model. The cross-partial derivative terms introduced by the anisotropic orientations were taken as source/sinks terms which can be easily handled by differed correction method. This method improves the diagonal dominance condition and raises the numerical accuracy and numerical stability.
渗流 / 各向异性 / 延迟修正 / 数值模拟 {{custom_keyword}} /
seepage flow / anisotropic / deferred correction method / numerical simulation {{custom_keyword}} /
[1]陶文铨. 数值传热学(第二版)[M]. 西安:西安交通大学出版社. 2001.5. [2]陶文铨. 计算传热学的近代进展[M]. 北京:科学出版社. 2000.6. [3]Hayase T, Humphery J A C. A consistently formulated QUICK scheme for fast and stable convergence using finite volume iterative calcution procedure[J]. Journal of Computational Physics. 1992.1:108-118. [4]Khosla P K, Rubin S G. A diagonally dominant second order accurate implicit scheme. Computers & Fluids. 1974.2: 207-209 [5]柏威,鄂学全. 基于非结构化同位网格的SIMPLE算法[J]. 计算力学学报. 2003.12:702-710. [6]李海滨,扬弘,冯国泰. 应用高精度差分格式求解Euler方程[J]. 哈尔滨工业大学学报. 2001.4:144-147. [7]李连侠. 非结构化网格下随机地下水模拟的非平稳谱方法及其并行算法研究[D]. 成都:四川大学,2007. [8]周志芳,王锦国. 裂隙介质水动力学[M]. 北京:中国水利水电出版社. 2004.1.
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