AI 中文总结
针对高对比度多孔介质中两相流模拟问题，提出将物理保持隐式压力显式饱和度格式与广义多尺度有限元方法结合的自适应多尺度方法，通过自适应更新策略及局部后处理保证物理性质，实验验证了方法有效性。
AI 中文摘要
本文提出了一种用于高对比度多孔介质中不可压缩且不混溶两相流的自适应物理保持多尺度方法。该方法将物理保持隐式压力显式饱和度格式（P - IMPES）与混合约束能量最小化广义多尺度有限元方法相结合。核心算法组件是饱和度相关系数的自适应更新策略。由于有效渗透率\(\kappa_n=\lambda_t(S_w^n)K\)通过总迁移率依赖于演化的饱和度，引入自适应更新算法，监测迁移率加权系数变化，仅在超过规定容差时重新生成多尺度空间。还使用局部后处理步骤恢复细网格质量守恒。文中进行了分析，证明了两相的局部守恒、相公式的无偏性以及在合适CFL条件下的界保持。对于平流主导情况，建立了速度和饱和度误差估计。不同高对比度渗透率场的数值实验证实了该方法的物理性质，表明较小的自适应容差可改善饱和度近似同时避免多尺度空间的不必要更新。
英文摘要
In this paper, we propose an adaptive physics-preserving multiscale method for incompressible and immiscible two-phase flow in high-contrast porous media. The method couples a physics-preserving implicit-pressure explicit-saturation scheme (P-IMPES) with the mixed constraint energy minimizing generalized multiscale finite element method. The core algorithmic component is an adaptive update strategy for the saturation-dependent coefficient. Since the effective permeability \(κ_n=λ_t(S_w^n)K\) depends on the evolving saturation through the total mobility, we introduce an adaptive update algorithm that monitors the variation of the mobility-weighted coefficient and regenerates the multiscale spaces only when a prescribed tolerance is exceeded. A local postprocessing step is further used to recover fine-grid mass conservation. The analysis is a central part of the paper. We prove local conservation for both phases, the unbiased property of the phase formulation, and bounds preservation under a suitable CFL condition. For the advection-dominated case, we establish velocity and saturation error estimates, which clearly identify the contributions from the adaptive tolerance, the coarse mesh size, the spectral approximation, and the front-layer error. Numerical experiments on different high-contrast permeability fields confirm the physical properties of the method and show that smaller adaptive tolerances improve the saturation approximation while avoiding unnecessary updates of the multiscale spaces.
Comments33 pages, 9 figures, and 2 tables
