Seminar
Numerical methods for solving the Cahn-Hilliard equation and its applicability to mixtures of isotropic and nematic flows with anchoring effects
Tuesday, October 13, 2015 10:00 AM;
JGU Mainz, Mathematics, Hilbert-Raum
Speaker: Giordano Tierra; Mathematical Institute, Charles University, Prague, Czech Republic
The study of interfacial dynamics between two dierent components has become the key role to understand the
behavior of many interesting systems, with applications in science, engineering, and industry. The Cahn-Hilliard
model was originally introduced by Cahn and Hilliard to describe the complicated phase separation and coarsening
phenomena in the mixture of dierent
uids, solid or gas where only two dierent concentration phases can exist
stably.
In the rst part of the seminar, I will present dierent numerical schemes to approximate the Cahn-Hilliard model,
showing the advantage and disadvantages of each scheme. In particular, I will focus on the study of the constraints
on the physical and discrete parameters that can appear to assure the energy-stability, unique solvability and, in the
case of nonlinear schemes, the convergence of Newton's method to the nonlinear schemes. Moreover, an adaptive time
stepping algorithm will be presented and the behavior of the schemes will be compared through several computational
experiments.
In the second part of the seminar, I will focus on a diuse interface approach to represent mixtures composed by
isotropic
uids and nematic liquid crystals. I will present new linear unconditionally energy-stable splitting schemes
that take into account viscous, mixing, nematic and anchoring eects. This formulation allows us to split the computa-
tion of the three pairs of unknowns (velocity-pressure, phase eld-chemical potential and director vector-equilibrium)
in three dierent steps. Finally, I will present several numerical simulations to illustrate the correct behavior of the
proposed numerical schemes and to show the dependence of the dynamics on the dierent types of anchoring eects
that can be considered.
This contribution is based on joint work with Francisco Guillen-Gonzalez (Universidad de Sevilla, Spain) and Mara
Angeles Rodrguez-Bellido (Universidad de Sevilla, Spain).
Calendar
Contact
- Scientific Coordinator of the TRR 146
- Dr. Giovanni Settanni
- Staudingerweg 9
- D-55128 Mainz
- trr146tescm-LX@GRSfnzuni-mainz.de