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

TL;DR

This paper introduces a multilevel nonlinear multigrid solver for two-phase flow in porous media with wells, improving computational efficiency on unstructured grids by using an aggregation-based coarsening algorithm.

Contribution

It develops a novel aggregation algorithm that enhances multigrid methods for multiphase flow simulations with wells, outperforming Newton's method in speed.

Findings

FAS solver is at least 35% faster than Newton's method on benchmark problems.

The solver effectively handles unstructured grids with perforated wells.

Performance improves with larger CFL numbers.

Abstract

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.