Consistent MPFA Discretization for Flow in the Presence of Gravity
Consistent MPFA Discretization for Flow in the Presence of Gravity
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DOI：
10.1029/2019wr025384
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发表时间：
2019-12
影响因子：
5.4
通讯作者：
M. Starnoni;I. Berre;E. Keilegavlen;J. Nordbotten
中科院分区：
文献类型：
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作者：
M. Starnoni;I. Berre;E. Keilegavlen;J. Nordbotten
在工业中用于离散两相达西流方程中的重力项的标准做法是应用逆风策略。在本文中，我们表明，这可能会给一个持久的非物理通量场和不正确的压力分布。作为这个问题的解决方案，我们提出了一个新的一致的离散流，称为引力一致的多点通量近似（GCMPFA），这是有效的单相和两相流。离散化是基于这样的想法，即流方程中的引力项被视为离散通量算子的一部分，而不是右手边。在这里，通过在MPFA构造中求解的局部线性系统中引入一组额外的右手边，将传统的将压力表示为势的公式扩展到包括重力的情况，从而获得了关于单元中心重力跳跃的通量表达式。数值算例显示了该方法的收敛性，提供了单相和两相流。对于两相流，我们展示了我们的新方法如何能够消除使用标准迎风格式时产生的非物理通量，从而收敛到正确的压力分布。
A standard practice used in the industry to discretizing the gravity term in the two‐phase Darcy flow equations is to apply an upwind strategy. In this paper, we show that this can give a persistent unphysical flux field and an incorrect pressure distribution. As a solution to this problem, we present a new consistent discretization of flow, termed Gravitationally Consistent Multipoint Flux Approximation (GCMPFA), which is valid for both single‐ and two‐phase flows. The discretization is based on the idea that the gravitational term in the flow equations is treated as part of the discrete flux operator and not as a right‐hand side. Here, the traditional formulation representing pressure as a potential is extended to the case including gravity by introducing an additional set of right‐hand side to the local linear system solved in the MPFA construction, thus obtaining an expression of the fluxes in terms of jumps in cell‐center gravities. Numerical examples showing the convergence of the method are provided for both single‐ and two‐phase flows. For two‐phase flow, we show how our new method is capable of eliminating the unphysical fluxes arising when using a standard upwind scheme, thus converging to the correct pressure distribution.