论文标题
高度异质的多孔介质中，基于物理保留的多尺度方法的多尺度方法
Physics-preserving IMPES based multiscale methods for immiscible two-phase flow in highly heterogeneous porous media
论文作者
论文摘要
在本文中，我们提出了一种保护物理学的多尺度方法，以解决不混溶的两相流问题，该方法被建模为由达西定律和大众保护方程组成的耦合系统。我们使用新的物理含义的隐式压力显式饱和（P-impes）方案，以维持这两个阶段的局部质量保护。此外，该方案是公正的，如果时间步长小于某个值，则两个阶段的饱和度都是限制的。更新速度时，MGMSFEM通过计算粗网格上的未知数来充当有效的求解器。我们遵循拆分Techinque的操作来处理两相流。特别是，我们使用上风策略明确迭代饱和度，并利用MGMSFEM在粗网格上使用脱钩系统来计算速度。为了显示所提出方法的效率和鲁棒性，我们设计了一组有趣的实验。还包括严格的分析，以作为该方法的理论基础，该方法通过数值结果很好地验证。模拟和分析都表明该方法在准确性和计算成本之间达到了良好的平衡。
In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and mass conservation equations. We use a new Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme in order to maintain the local conservation of mass for both phases. Besides, this scheme is unbiased and if the time step is smaller than a certain value, the saturation of both phases are bounds-preserving. When updating velocity, MGMsFEM serves as an efficient solver by computing the unknowns on a coarse grid. We follow the operation splitting techinque to deal with the two-phase flow. In particular, we use an upwind strategy to iterate the saturation explicitly and the MGMsFEM is utilized to compute velocity with a decoupled system on a coarse mesh. To show the efficiency and robustness of the proposed method, we design a set of interesting experiments. A rigorous analysis is also included to serve as a theoretical base of the method, which is well verified by the numerical results. Both simulations and analysis indicate that the method attains a good balance between accuracy and computation cost.
