Relationships among some locally conservative discretization methods which handle discontinuous coefficients
Relationships among some locally conservative discretization methods which handle discontinuous coefficients
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DOI：
10.1007/s10596-005-1815-9
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发表时间：
2004-12
影响因子：
2.5
通讯作者：
R. A. Klausen;T. Russell
中科院分区：
文献类型：
--
作者：
R. A. Klausen;T. Russell
本文介绍了一些适用于非均质椭圆方程的数值方法与油藏模拟应用之间的关系。讨论的方法有经典混合有限元法（MFEM）、控制体混合有限元法（CVMFEM）、支持算子法（SOM）、增强单元中心有限差分法（ECCFDM）和多点通量逼近（MPFA）控制体法。这些方法都是局部质量保守的，并且处理具有各向异性和异质不连续渗透率的一般不规则网格。除此之外，这些方法在边缘压力方面具有共同的弱连续性，在某些情况下对应于拉格朗日乘子。看来最后一个属性是这些方法的基本共同品质。
This paper presents the relationships between some numerical methods suitable for a heterogeneous elliptic equation with application to reservoir simulation. The methods discussed are the classical mixed finite element method (MFEM), the control-volume mixed finite element method (CVMFEM), the support operators method (SOM), the enhanced cell-centered finite difference method (ECCFDM), and the multi-point flux-approximation (MPFA) control-volume method. These methods are all locally mass conservative, and handle general irregular grids with anisotropic and heterogeneous discontinuous permeability. In addition to this, the methods have a common weak continuity in the pressure across the edges, which in some cases corresponds to Lagrange multipliers. It seems that this last property is an essential common quality for these methods.