Improving the convergence behaviour of a fixed‐point‐iteration solver for multiphase flow in porous media. (18th December 2016)

• Record Type: Journal Article
• Authors: Salinas, P.; Pavlidis, D.; Xie, Z.; Adam, A.; Pain, C. C.; Jackson, M. D.
• Is Part Of: International journal for numerical methods in fluids. Volume 84:Number 8(2017)
• Page Start: 466
• Page End: 476
• Publication Date: 2016-12-18
• Subjects: nonlinear solvers -- fixed point iteration -- multiphase flow -- porous media -- implicit time stepping -- Darcy flow; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4357
• Languages: English
• ISSNs: 0271-2091

Abstract

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. Abstract : Improving the convergence behaviour of a fixed‐point‐iteration solver for multiphase flow in porous media: Development of a more robust non‐linear solver with increase effective convergence rate to admit large Courant numbers in multiphase flow in porous media by adding strengthening the coupling between velocity and saturation, adding vanishing artificial diffusion and calculating an efficient backtracking parameter.