Adaptive time-stepping for Cahn-Hilliard-type equations with application to diffuse-interface tumor-growth models

X. Wu, G. J. Van Zwieten, K.G. Van Der Zee, G. Simsek

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    1 Citation (Scopus)

    Abstract

    Many tumor-growth phenomena can be considered as multiphase problems. Employing the continuum theory of mixtures, phase-field tumor-growth models can be derived with diffuse interfaces. The chosen form of the Helmholtz free-energy leads to equations of the Cahn-Hilliard type. Such nonlinear fourth-order partial-differential equations are time-dependent, and their solutions exhibit alternating fast and slow variations in time. It is therefore of prime importance to use adaptive time-stepping to efficiently simulate the entire dynamics of the system [5]. In this contribution, we consider a thermodynamically consistent four-species model of tumor growth in which the energy is non-increasing and total mass is conserved [6]. In order to inherit these two main characteristics of the system at the discrete level, we propose a gradient-stable time-stepping scheme with second-order accuracy [8]. Mixed finite elements are used for spatial discretization. For this discretization, we discuss various adaptive time-stepping strategies in time. Furthermore, we present illustrative numerical results.

    Original languageEnglish
    Title of host publication6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013
    EditorsJ.P. Moitinho de Almeida, P. Diez, C. Tiago, N. Parés
    Pages705-709
    Number of pages5
    Publication statusPublished - 1 Dec 2013
    Event6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013 - Lisbon, Portugal
    Duration: 3 Jun 20135 Jun 2013

    Conference

    Conference6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013
    CountryPortugal
    CityLisbon
    Period3/06/135/06/13

    Keywords

    • Adaptive time-stepping
    • Cahn-hilliard equation
    • Diffuse- interface tumor-growth model
    • Second-order time-accurate algorithms

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