Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media
Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media
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DOI：
10.1007/s10596-005-5665-2
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发表时间：
2005-03
影响因子：
2.5
通讯作者：
J. Nordbotten;I. Aavatsmark
中科院分区：
文献类型：
--
作者：
J. Nordbotten;I. Aavatsmark
控制体积方法经常用于多孔介质流动。本文举例说明了一种方法，即多点通量逼近法 (MPFA)，如何无法满足强各向异性或网格偏斜的最大原理，并提出了均匀介质中均匀平行四边形网格的单调性属性成立的条件。所开发的条件适用于 2D 中的任何 9 点方案或 3D 中的 27 点方案，并且当该方法生成不是 M 矩阵的系统矩阵时非常有用。
Control volume methods are frequently used in porous media flow. This article gives an example on how one method, the Multipoint Flux Approximation method (MPFA), fails to satisfy the maximum principle for strong anisotropies or grid skewnesses, and develops conditions for when the monotonicity property holds for uniform parallelogram grids in homogeneous media. The conditions developed are applicable to any nine-point scheme in 2D or 27-point scheme in 3D, and is useful when the method produces a system matrix which is not an M-matrix.