An $H^2$ convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn–Hilliard equation

2016 ◽  
Vol 14 (2) ◽  
pp. 489-515 ◽  
Author(s):  
Jing Guo ◽  
Cheng Wang ◽  
Steven M. Wise ◽  
Xingye Yue
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Second Order ◽  
Hilliard Equation ◽  
Convex Splitting ◽  
Cahn Hilliard Equation

scholarly journals The Cahn–Hilliard Equation with Generalized Mobilities in Complex Geometries

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jaemin Shin ◽  
Yongho Choi ◽  
Junseok Kim
Keyword(s):  
Growth Rate ◽  
Finite Difference ◽  
Difference Scheme ◽  
Pore Size ◽  
Finite Difference Scheme ◽  
Numerical Experiments ◽  
Complex Geometries ◽  
Hilliard Equation ◽  
Controlled Porosity ◽  
Cahn Hilliard Equation

In this study, we apply a finite difference scheme to solve the Cahn–Hilliard equation with generalized mobilities in complex geometries. This method is conservative and unconditionally gradient stable for all positive variable mobility functions and complex geometries. Herein, we present some numerical experiments to demonstrate the performance of this method. In particular, using the fact that variable mobility changes the growth rate of the phases, we employ space-dependent mobility to design a cylindrical biomedical scaffold with controlled porosity and pore size.

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