Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

Haijian Yang, Shuyu Sun, Chao-he Yang

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalJournal of Computational Physics
Volume332
DOIs
StatePublished - Dec 10 2016

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