title: Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models.
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.
authors.affiliation: Multiscale Engineering Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
authors.forename: X
authors.initials: X
authors.lastname: Wu
authors.forename: G J
authors.initials: GJ
authors.lastname: van Zwieten
authors.forename: K G
authors.initials: KG
authors.lastname: van der Zee
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D008962:Models, Theoretical; D009369:Neoplasms / Q000378:metabolism*
keywords: Cahn-Hilliard equation; artificial stabilization; convex-concave splitting; diffuse-interface models; second-order accurate schemes; tumor-growth models