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Improving the convergence behaviour of a fixed‐point‐iteration solver for multiphase flow in porous media
Author(s) -
Salinas P.,
Pavlidis D.,
Xie Z.,
Adam A.,
Pain C. C.,
Jackson M. D.
Publication year - 2016
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4357
Subject(s) - solver , discretization , rate of convergence , mathematics , convergence (economics) , acceleration , nonlinear system , mathematical optimization , fixed point iteration , computer science , fixed point , mathematical analysis , physics , classical mechanics , channel (broadcasting) , computer network , quantum mechanics , economics , economic growth
Summary A new method to admit large Courant numbers in the numerical simulation of multiphase flow is presented. The governing equations are discretized in time using an adaptive θ ‐method. However, the use of implicit discretizations does not guarantee convergence of the nonlinear solver for large Courant numbers. In this work, a double‐fixed point iteration method with backtracking is presented, which improves both convergence and convergence rate. Moreover, acceleration techniques are presented to yield a more robust nonlinear solver with increased effective convergence rate. The new method reduces the computational effort by strengthening the coupling between saturation and velocity, obtaining an efficient backtracking parameter, using a modified version of Anderson's acceleration and adding vanishing artificial diffusion. © 2016 The Authors. International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd.