Finite difference methods for modeling porous media flows
Finite difference methods for modeling porous media flows
复制标题
多孔介质流建模的有限差分法
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
S. Schaffer
中科院分区：
文献类型：
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作者：
B. Das;S. Steinberg;Susan Weber;S. Schaffer
本研究的目的是确定什么样的有限差分算法是最好的用于数值模拟的二维单相饱和多孔介质流动时，模型具有非对角对称张量的流动性（或水力传导率），具有非平凡的跳跃不连续沿着线，不对齐的坐标轴。这些问题在许多建模情况下自然会出现，此外，当使用自适应网格研究更简单的问题时，答案是令人惊讶的，最简单的有限差分方法，称为线性平均的MAC方案，在广泛的问题上几乎与大多数其他算法一样好。一种新的算法，称为全谐波平均方案，使用成本明显更高，但在某些有趣的情况下确实比最简单的方案性能更好。最简单的有限差分法相比，从文献中采取的一些有限元模拟;有限差分算法执行better.Many的结论的文件休息测试的算法上的一类新的问题的解析解。该问题具有非对角迁移率张量，并且可以具有任意高度的跳跃间断。
The purpose of this study is to determine what finite-difference algorithms are best used in numerical simulation of two-dimensional single-phase saturated porous media flows when the models have a nondiagonal symmetric tensor for the mobility (or hydraulic conductivity) that has nontrivial jump discontinuities along lines that are not aligned with the coordinate axes. Such problems arise naturally in many modeling situations and, in addition, when simpler problems are studied using adaptive grids.The answer is surprising, the simplest finite-difference method, called the MAC Scheme with Linear Averaging, performs nearly as well as most other algorithms over a wide range of problems. A new algorithm, called the Full Harmonic Averaged Scheme, is significantly more costly to use, but does perform better than the simplest scheme in certain interesting cases. The simplest finite-difference method is compared to some finite-element simulations taken from the literature; the finite-difference algorithm performs better.Many of the conclusions of the paper rest on testing the algorithms on a new class of problems with analytic solutions. The problems have a nondiagonal mobility tensor and can have a jump discontinuity of arbitrary height.