scholarly journals An energy stable fourth order finite difference scheme for the Cahn–Hilliard equation

2019 ◽  
Vol 362 ◽  
pp. 574-595 ◽  
Author(s):  
Kelong Cheng ◽  
Wenqiang Feng ◽  
Cheng Wang ◽  
Steven M. Wise
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Fourth Order ◽  
Finite Difference Scheme ◽  
Hilliard Equation ◽  
Energy Stable ◽  
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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