Finite volume methods are prevalent in reservoir simulation due to their mass conservation properties and their ability to handle complex grids. However, a simple and consistent finite volume method for elasticity was unavailable until the recently developed two-point stress approximation finite volume method (TPSA). In this work, we show how to couple TPSA to an established flow simulator, using OPM Flow as our primary example. Due to this choice of numerical methods, the coupling is naturally handled at the cell centers, without requiring interpolation operators. We propose a fixed stress coupling scheme and reuse algebraic multi-grid preconditioners, which are known to be effective for two-point flux finite volume methods. Numerical examples illustrate the flexibility of the approach and we showcase how the introduction of solid mechanics impacts the behavior of compartmentalized flow systems.

翻译：有限体积法因其质量守恒特性及处理复杂网格的能力，在油藏模拟中应用广泛。然而，针对弹性力学的简单且一致的有限体积方法长期缺失，直至最近发展的两点应力近似有限体积法（TPSA）才填补了这一空白。本文展示了如何将TPSA与成熟的流动模拟器耦合，并以OPM Flow为主要示例。基于所选数值方法，耦合过程自然地在单元中心处理，无需插值算子。我们提出了一种固定应力耦合方案，并复用了代数多重网格预处理器——该方法已知对两点通量有限体积法具有高效性。数值算例证明了该方法的灵活性，并展示了固体力学引入如何影响分区流动系统的行为特征。