Open-source MATLAB implementation of consistent discretisations on complex grids
Open-source MATLAB implementation of consistent discretisations on complex grids
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DOI：
10.1007/s10596-011-9244-4
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发表时间：
2012-03
影响因子：
2.5
通讯作者：
Knut-Andreas Lie;S. Krogstad;I. Ligaarden;J. Natvig;H. Nilsen;B. Skaflestad
中科院分区：
文献类型：
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作者：
Knut-Andreas Lie;S. Krogstad;I. Ligaarden;J. Natvig;H. Nilsen;B. Skaflestad
断层、裂缝或侵蚀等地貌的精确地质建模需要几何形状灵活的网格。这种网格通常包含多面体单元和复杂的网格-单元连接。多面体网格的网格表示反过来又影响地下水流模拟数值方法的有效实施。众所周知，传统的两点通量近似方法只对K-正交网格是相容的，因此在一般情况下是不收敛的。近年来，有显着的研究一致和收敛的方法，包括混合，多点和模仿离散化方法。同样，基于分层粗化网格的多尺度方法也受到了广泛的关注。本文没有提出新的数学方法，而是提出了一个开源的Matlab ®工具包，可用作油藏模拟中（新）离散化和求解方法的有效测试平台。该工具包的目的是支持可重复的研究和简化一般非结构化网格，包括特别是角点和2.5D PEBI网格上的新离散化和求解方法的开发，验证和确认以及测试和比较。该工具包包括一组数据结构和例程，用于创建、操作和可视化岩石物理数据、流体模型和（非结构化）网格，包括支持行业标准输入格式，以及计算单相和多相（不可压缩）流的例程。我们审查的工具包的主要功能，并讨论了一个通用的拟态制剂，包括许多已知的离散化方法，包括标准的两点法以及一致和收敛的多点和拟态方法。除了核心例程和数据结构外，该工具包还包含实现更高级求解器和功能的附加模块。在这里，我们展示了多尺度方法和伴随方法用于优化威尔斯的速度和位置的例子。
Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect to geometry. Such grids generally contain polyhedral cells and complex grid-cell connectivities. The grid representation for polyhedral grids in turn affects the efficient implementation of numerical methods for subsurface flow simulations. It is well known that conventional two-point flux-approximation methods are only consistent forK-orthogonal grids and will, therefore, not converge in the general case. In recent years, there has been significant research into consistent and convergent methods, including mixed, multipoint and mimetic discretisation methods. Likewise, the so-called multiscale methods based upon hierarchically coarsened grids have received a lot of attention. The paper does not propose novel mathematical methods but instead presents an open-sourceMatlab® toolkit that can be used as an efficient test platform for (new) discretisation and solution methods in reservoir simulation. The aim of the toolkit is to support reproducible research and simplify the development, verification and validation and testing and comparison of new discretisation and solution methods on general unstructured grids, including in particular corner point and 2.5D PEBI grids. The toolkit consists of a set of data structures and routines for creating, manipulating and visualising petrophysical data, fluid models and (unstructured) grids, including support for industry standard input formats, as well as routines for computing single and multiphase (incompressible) flow. We review key features of the toolkit and discuss a generic mimetic formulation that includes many known discretisation methods, including both the standard two-point method as well as consistent and convergent multipoint and mimetic methods. Apart from the core routines and data structures, the toolkit contains add-on modules that implement more advanced solvers and functionality. Herein, we show examples of multiscale methods and adjoint methods for use in optimisation of rates and placement of wells.