AN EFFICIENT AND ROBUST METHOD FOR SIMULATING TWO-PHASE GEL DYNAMICS

Grady B. Wright

doi:10.1137/070695927

AN EFFICIENT AND ROBUST METHOD FOR SIMULATING TWO-PHASE GEL DYNAMICS

2008-01-01

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DOI：10.1137/070695927

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We develop a computational method for simulating models of gel dynamics where the gel is described by two phases: a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and a volume-averaged incompressibility constraint, which we discretize with finite differences/volumes. The momentum and incompressibility equations present the greatest numerical challenges since (i) they involve partial derivatives with variable coefficients that can vary quite significantly throughout the domain ( when the phases separate), and (ii) their approximate solution requires the inversion of a large linear system of equations. For solving this system, we propose a box-type multigrid method to be used as a preconditioner for the generalized minimum residual (GMRES) method. Through numerical experiments of a model problem, which exhibits phase separation, we show that the computational cost of the method scales nearly linearly with the number of unknowns and performs consistently well over a wide range of parameters. For solving the transport equation, we use a conservative finite-volume method for which we derive stability bounds.

Keywords:

multiphase flow

mixture theory

multigrid

Vanka relaxation

coupled relaxation

box relaxation

Krylov

GMRES

preconditioning

AN EFFICIENT AND ROBUST METHOD FOR SIMULATING TWO-PHASE GEL DYNAMICS

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