The Penrose-Fife phase-field model with coupled dynamic boundary conditions

2014 ◽  
Vol 34 (10) ◽  
pp. 4259-4290 ◽  
Author(s):  
Alain Miranville ◽  
Elisabetta Rocca ◽  
Giulio Schimperna ◽  
Antonio Segatti
Keyword(s):  
Boundary Conditions ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

scholarly journals A DDFV method for a Cahn−Hilliard/Stokes phase field model with dynamic boundary conditions

2017 ◽  
Vol 51 (5) ◽  
pp. 1691-1731 ◽  
Author(s):  
Franck Boyer ◽  
Flore Nabet
Keyword(s):  
Boundary Conditions ◽  
Energy Inequality ◽  
Splitting Method ◽  
Phase Field Model ◽  
Nonlinear Boundary Conditions ◽  
Diffuse Interface ◽  
Dynamic Boundary Conditions ◽  
Two Phase ◽  
Discrete Equations ◽  
Dynamic Boundary

In this paper we propose a “Discrete Duality Finite Volume” method (DDFV for short) for the diffuse interface modelling of incompressible two-phase flows. This numerical method is, conservative, robust and is able to handle general geometries and meshes. The model we study couples the Cahn−Hilliard equation and the unsteady Stokes equation and is endowed with particular nonlinear boundary conditions called dynamic boundary conditions. To implement the scheme for this model we have to derive new discrete consistent DDFV operators that allows an energy stable coupling between both discrete equations. We are thus able to obtain the existence of a family of solutions satisfying a suitable energy inequality, even in the case where a first order time-splitting method between the two subsystems is used. We illustrate various properties of such a model with some numerical results.

scholarly journals Phase-field systems with nonlinear coupling and dynamic boundary conditions

2010 ◽  
Vol 72 (5) ◽  
pp. 2375-2399 ◽  
Author(s):  
Cecilia Cavaterra ◽  
Ciprian G. Gal ◽  
Maurizio Grasselli ◽  
Alain Miranville
Keyword(s):  
Boundary Conditions ◽  
Phase Field ◽  
Nonlinear Coupling ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Field Systems

ATTRACTORS FOR A CAGINALP MODEL WITH A LOGARITHMIC POTENTIAL AND COUPLED DYNAMIC BOUNDARY CONDITIONS

2013 ◽  
Vol 11 (06) ◽  
pp. 1350024 ◽  
Author(s):  
MONICA CONTI ◽  
STEFANIA GATTI ◽  
ALAIN MIRANVILLE
Keyword(s):  
Boundary Conditions ◽  
Phase Field Model ◽  
Logarithmic Potential ◽  
Dynamic Boundary Conditions ◽  
Exponential Attractors ◽  
Dynamic Boundary ◽  
Suitable Definition ◽  
Finite Fractal Dimension ◽  
Definition Of ◽  
Longtime Behavior

We study the longtime behavior of the Caginalp phase-field model with a logarithmic potential and dynamic boundary conditions for both the order parameter and the temperature. Due to the possible lack of distributional solutions, we deal with a suitable definition of solutions based on variational inequalities, for which we prove well-posedness and the existence of global and exponential attractors with finite fractal dimension.

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