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.

翻译：开发了一种用于多射孔井驱动的两相流与输运问题的全近似格式(FAS)非线性多重网格求解器。该求解器是对我们先前针对扩散与输运问题所开发的FAS求解器的扩展。由于粗化算法基于代数聚类技术，该求解器适用于定义在非结构化网格上的离散问题。为构建能更好捕捉井附近径向流的粗基函数，需要确保射孔井单元不接近粗单元界面的粗网格。本文提出一种利用单元连接图中井单元位置的聚类算法来实现该目标。通过数值算例将FAS求解器与牛顿法在基准问题上进行对比，特别地，针对精化版本的SAIGUP模型，当时间步的CFL数大于10时，FAS求解器计算速度至少比牛顿法快35%。