Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models

X. Wu, G.J. van Zwieten, K.G. van der Zee

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    Abstract

    We present unconditionally energy-stable second-order time-accurate schemes for diffuse-interface (phase-field) models; in particular, we consider the Cahn–Hilliard equation and a diffuse-interface tumor-growth system consisting of a reactive Cahn–Hilliard equation and a reaction–diffusion equation. The schemes are of the Crank–Nicolson type with a new convex–concave splitting of the free energy and an artificial-diffusivity stabilization. The case of nonconstant mobility is treated using extrapolation. For the tumor-growth system, a semi-implicit treatment of the reactive terms and additional stabilization are discussed. For suitable free energies, all schemes are linear. We present numerical examples that verify the second-order accuracy, unconditional energy-stability, and superiority compared with their first-order accurate variants.
    Original languageEnglish
    Pages (from-to)180-203
    JournalInternational Journal for Numerical Methods in Biomedical Engineering
    Volume30
    Issue number2
    DOIs
    Publication statusPublished - Feb 2014

    Bibliographical note

    Special issue paper - numerical methods and applications of multi-physics in biomechanical modeling

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