A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids
A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids
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DOI：
10.1016/j.jcp.2010.09.012
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
H. A. Friis;M. Edwards
中科院分区：
文献类型：
--
作者：
H. A. Friis;M. Edwards
提出了一种新的以胞心为中心的有限体积格式，用于求解任意非结构三角形上多孔介质地下流动的一般全张量压力方程。与之前的方案相比，新方案是通量连续的，并且在每个子单元上具有全压力支撑（FPS），每个控制体积子界面上施加连续压力。早期的方法采用三角形压力支撑（TPS），压力和通量逐点连续，这导致正交范围更有限。通过m矩阵分析，确定了该格式具有局部离散极大值原则的边界。并给出了该格式为正定的条件。针对非结构化三角形网格，包括高度不规则网格，给出了一系列计算实例，并将新的FPS方案与早期的点向连续TPS公式进行了比较。早期的点向TPS方法可以在涉及强全张量各向异性的问题中诱导强伪振荡，其中m矩阵条件被违反，并且可以在这种情况下导致解耦。研究了非结构化胞心解耦。与TPS相比，新的FPS公式导致了很好的解决方案，基本上没有虚假振荡。在所有的收敛测试中，压力和速度的收敛性能都得到了很大程度的改善。这对于涉及高各向异性比率的问题尤其重要。此外，新公式证明了对一个升级的例子非常有益，其中对某些正交点的收敛性增强非常显著，清楚地显示了新公式的进一步优势。
A new family of cell-centered finite-volume schemes is presented for solving the general full-tensor pressure equation of subsurface flow in porous media on arbitary unstructured triangulations. The new schemes are flux continuous and have full pressure support (FPS) over each subcell with continuous pressure imposed across each control-volume sub-interface, in contrast to earlier formulations. The earlier methods are point-wise continuous in pressure and flux with triangle-pressure-support (TPS) which leads to a more limited quadrature range. An M-matrix analysis identifies bounding limits for the schemes to posses a local discrete maximum principle. Conditions for the schemes to be positive definite are also derived. A range of computational examples are presented for unstructured triangular grids, including highly irregular grids, and the new FPS schemes are compared against the earlier pointwise continuous TPS formulations. The earlier pointwise TPS methods can induce strong spurious oscillations for problems involving strong full-tensor anisotropy where the M-matrix conditions are violated, and can lead to decoupled solutions in such cases. Unstructured cell-centered decoupling is investigated. In contrast to TPS, the new FPS formulation leads to well resolved solutions that are essentially free of spurious oscillations. A substantial degree of improved convergence behavior, for both pressure and velocity, is also observed in all convergence tests. This is particularly important for problems involving high anisotropy ratios. Also the new formulation proves to be highly beneficial for an upscaling example, where enhancement of convergence is highly significant for certain quadrature points, clearly demonstrating further advantages of the new formulation.