Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
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结构化和非结构化网格上的多尺度有限体积 CVD-MPFA 配方
DOI：
10.1137/140953691
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Sadok Lamine
中科院分区：
文献类型：
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作者：
Elliot Parramore;M. Edwards;M. Pal;Sadok Lamine
本文介绍了四边形和三角形非结构网格的有限体积多尺度方法的发展。发展了达西通量近似族，用于达西定律和质量守恒所产生的一般张量压力方程的一致近似。这些格式是控制体积分布的(CVD)，流动变量和岩石性质共享相同的控制体积位置，并由多点流量族公式(CVD-MPFA)组成。该格式被用来发展一种基于CVD-MPFA的多尺度有限体积(MSFV)格式，可同时适用于二维结构网格和非结构网格。基函数是MSFV方法的关键组成部分，是一组局部解，通常根据Dirichlet边界条件定义。笛卡尔网格Dirichlet基函数的推广[P.Jenny，S.H.Lee，和H.A.Tchelepi，J.Comput.Phys，187(2003)，pp.47--67]这里介绍了非结构网格。虽然从笛卡尔网格到非结构网格的过渡在很大程度上是成功的，但使用Dirichlet基函数仍然可以导致压力场在强非均质性区域表现出虚假振荡。为了改进压力场的解，提出了新的基函数，其中几乎所有地方都施加了Neumann边界条件，除了仍然由Dirichlet值指定的拐角。
This paper presents the development of finite-volume multiscale methods for quadrilateral and triangular unstructured grids. Families of Darcy-flux approximations have been developed for consistent approximation of the general tensor pressure equation arising from Darcy's law together with mass conservation. The schemes are control-volume distributed (CVD) with flow variables and rock properties sharing the same control-volume location and are comprised of a multipoint flux family formulation (CVD-MPFA). The schemes are used to develop a CVD-MPFA based multiscale finite-volume (MSFV) formulation applicable to both structured and unstructured grids in two dimensions. The basis functions are a key component of the MSFV method, and are a set of local solutions, usually defined subject to Dirichlet boundary conditions. A generalization of the Cartesian grid Dirichlet basis functions described in [P. Jenny, S. H. Lee, and H. A. Tchelepi, J. Comput. Phys., 187 (2003), pp. 47--67] is presented here for unstructured grids. Whilst the transition from a Cartesian grid to an unstructured grid is largely successful, use of Dirichlet basis functions can still lead to pressure fields that exhibit spurious oscillations in areas of strong heterogeneity. New basis functions are proposed in an attempt to improve the pressure field solutions where Neumann boundary conditions are imposed almost everywhere, except corners which remain specified by Dirichlet values.