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

    Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

    1 Citaat (Scopus)

    Samenvatting

    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.

    Originele taal-2Engels
    Titel6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013
    RedacteurenJ.P. Moitinho de Almeida, P. Diez, C. Tiago, N. Parés
    Pagina's705-709
    Aantal pagina's5
    StatusGepubliceerd - 1 dec 2013
    Evenement6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013 - Lisbon, Portugal
    Duur: 3 jun 20135 jun 2013

    Congres

    Congres6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013
    LandPortugal
    StadLisbon
    Periode3/06/135/06/13

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