Enriched multi-point flux approximation for general grids
Enriched multi-point flux approximation for general grids
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DOI：
10.1016/j.jcp.2007.09.021
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Qian-Yong Chen;J. Wan;Yahan Yang-;R. Mifflin
中科院分区：
文献类型：
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作者：
Qian-Yong Chen;J. Wan;Yahan Yang-;R. Mifflin
众所周知，两点通量近似，在大多数商业油藏模拟器中使用的数值格式，当网格不是K正交时具有O（1）误差。在过去的十年中，多点通量近似已被开发作为一种补救措施。然而，当各向异性非常强时，会出现非物理振荡。我们发现，振荡密切相关的压力梯度的近似通量计算。在本文中，我们提出了控制体积丰富的多点通量近似（EMPFA）的多边形和多面体网格上的一般扩散问题。非物理振荡没有观察到的现实和强各向异性的非均匀材料的属性描述的一个完整的张量。精确的线性解决方案恢复网格与非平面界面，并实现了一阶和二阶收敛的通量和标量未知数，分别。
It is well known that the two-point flux approximation, a numerical scheme used in most commercial reservoir simulators, has O(1) error when grids are not K-orthogonal. In the last decade, the multi-point flux approximations have been developed as a remedy. However, non-physical oscillations can appear when the anisotropy is really strong. We found out the oscillations are closely related to the poor approximation of pressure gradient in the flux computation. In this paper, we propose the control volume enriched multi-point flux approximation (EMPFA) for general diffusion problems on polygonal and polyhedral meshes. Non-physical oscillations are not observed for realistic and strongly anisotropic heterogeneous material properties described by a full tensor. Exact linear solutions are recovered for grids with non-planar interfaces, and a first and second order convergence are achieved for the flux and scalar unknowns, respectively.