2015-03-27

Energy stable integration of Allen-Cahn and Cahn-Hilliard equations

Prof. Dr. Bülent Karasözen, Middle East Technical University, Ankara (Turkey)

23 Apr 2015, 16:00–17:30; Location: S4|10-314

We consider Allen-Cahn and Cahn-Hilliard equations as phase fi eld models with constant and variable mobility. Both equations are discretized in space using symmetric interior penalty discontinuous Galerkin (SIPG) fi nite elements. Time discretization is performed by the energy stable average vector field (AVF) method for gradient systems like Allen-Cahn equation. We show that the fully discrete scheme satis fies the energy decreasing property. The numerical results for one and two dimensional Allen-Cahn and Cahn-Hilliard equations using adaptive stepping con firm that the discrete energy decreases monotonically, the phase separation and metastability phenomena can be observed and the ripening time is detected correctly for convex double well and non-convex logarithmic energy functionals.

Category: CE Seminar

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Technische Universität Darmstadt

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