标题： 多相流在多孔介质中基于聚合的非线性多重网格的多井建模 显示英文标题

标题： Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

摘要： 针对由带有多个穿孔的井驱动的两相流与输运问题，开发了一种基于全近似格式（FAS）的非线性多重网格求解器。这是对我们之前关于扩散和输运问题的FAS求解器工作的扩展。 该求解器适用于定义在非结构化网格上的离散问题，因为粗化算法是基于聚合和代数的。 为了构建能够更好地捕捉井附近径向流动的粗尺度基函数，期望穿孔井单元附近的粗网格元素界面不在粗单元界面附近。这通过本文提出的利用井单元在单元连通图中位置的聚合算法实现。 给出了FAS求解器与牛顿方法在基准问题上的比较数值例子。特别是，对于SAIGUP模型的细化版本，在CFL数大于10的时间步长上，FAS求解器至少比牛顿方法快35%。 显示英文摘要

摘要： A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.