Improving the convergence behaviour of a fixed-point-iteration solver for multiphase flow in porous media

Salinas, P., Pavlidis, D., Xie, Zhihua ORCID: https://orcid.org/0000-0002-5180-8427, Adam, A., Pain, C. C. and Jackson, M. D. 2017. Improving the convergence behaviour of a fixed-point-iteration solver for multiphase flow in porous media. International Journal for Numerical Methods in Fluids 84 (8) , pp. 466-476. 10.1002/fld.4357

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TJ Mechanical engineering and machinery
Publisher:	John Wiley & Sons
ISSN:	0271-2091
Funders:	Engineering and Physical Sciences Research Council (EPSRC)
Date of First Compliant Deposit:	27 January 2017
Date of Acceptance:	25 November 2016
Last Modified:	03 May 2023 11:19
URI:	https://orca.cardiff.ac.uk/id/eprint/97687

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