Parallel multilevel restricted Schwarz preconditioners for implicit simulation of subsurface flows with Peng-Robinson equation of state

TL;DR

This paper develops and analyzes scalable multilevel restricted Schwarz preconditioners for fully implicit simulation of subsurface flows with Peng-Robinson equation of state, demonstrating high efficiency and scalability on supercomputers.

Contribution

It introduces a family of multilevel restricted additive Schwarz methods tailored for large-scale subsurface flow simulations with Peng-Robinson EOS, enhancing parallel efficiency.

Findings

Achieved scalability to 8192 processors on Tianhe-2 supercomputer.

Demonstrated efficiency on standard benchmarks and realistic large-scale problems.

Developed preconditioners that improve convergence of Newton iterations.

Abstract

Parallel algorithms and simulators with good scalabilities are particularly important for large-scale reservoir simulations on modern supercomputers with a large number of processors. In this paper, we introduce and study a family of highly scalable multilevel restricted additive Schwarz (RAS) methods for the fully implicit solution of subsurface flows with Peng-Robinson equation of state in two and three dimensions. With the use of a second-order fully implicit scheme, the proposed simulator is unconditionally stable with the relaxation of the time step size by the stability condition. The investigation then focuses on the development of several types of multilevel overlapping additive Schwarz methods for the preconditioning of the resultant linear system arising from the inexact Newton iteration, and some fast solver technologies are presented for the assurance of the multilevel approach efficiency and scalability. We numerically show that the proposed fully implicit framework is highly efficient for solving both standard benchmarks as well as realistic problems with several hundreds of millions of unknowns and scalable to 8192 processors on the Tianhe-2 supercomputer.