Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 84, Issue 8, Pages 466-476Publisher
WILEY
DOI: 10.1002/fld.4357
Keywords
nonlinear solvers; fixed point iteration; multiphase flow; porous media; implicit time stepping; Darcy flow
Categories
Funding
- Innovate UK Octopus
- EPSRC Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents
- Horizon In-Vessel Melt Retention
- EPSRC ('Multi-Scale Exploration of Multiphase Physics in Flows' - MEMPHIS)
- TOTAL
- TOTAL Chairs programme at Imperial College
- EPSRC [EP/P013198/1, EP/M012794/1, EP/R005761/1, EP/K003976/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/R005761/1, EP/P013198/1, EP/K003976/1, EP/M012794/1] Funding Source: researchfish
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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 theta-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. (C) 2016 The Authors. International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd.
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