Author:
Nardean Stefano,Ferronato Massimiliano,Abushaikha Ahmad
Abstract
AbstractThis work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $$3\times 3$$
3
×
3
block-structured Jacobian matrix with a $$2\times 2$$
2
×
2
inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $$2\times 2$$
2
×
2
structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.
Funder
Qatar National Research Fund
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,Computational Theory and Mathematics,Computers in Earth Sciences,Computer Science Applications