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 . 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 . 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 . 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.
|Titel||6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013|
|Redacteuren||J.P. Moitinho de Almeida, P. Diez, C. Tiago, N. Parés|
|Status||Gepubliceerd - 1 dec 2013|
|Evenement||6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013 - Lisbon, Portugal|
Duur: 3 jun 2013 → 5 jun 2013
|Congres||6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013|
|Periode||3/06/13 → 5/06/13|