In this work we consider preconditioned iterative solution methods for numerical simulations of multiphase flow problems, modelled by the Cahn-Hilliard equation. We focus on diphasic flows and the construction and efficiency of a preconditioner for the algebraic systems arising from finite element discretizations in space and the θ-method in time. The preconditioner utilises to a full extent the algebraic structure of the underlying matrices and exhibits optimal convergence and computational complexity properties. Various numerical experiments, including large scale examples, are presented as well as performance comparisons with other solution methods.
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