
GPU-based Conjugated Gradient Solution for Phase Field ModelsGPU-based Conjugated Gradient Solution for Phase Field Models 125
The Allen-Cahn Eq. (5.3.4) is used to model the separation process of a
binary fl uid, in which the fl uid is decomposed into a fi ne-grained mixture
of particles. This process is known as spinodal decomposition (Badalassi
2003).
5.3.1 Discretization of the allen-cahn equation
In order to discretize Eq. (5.3.4), the fi nite difference method is used. The
discretization is done through the Crank-Nicholson scheme to obtain a
second-order accuracy in time. The fi nite difference method replaces the
derivatives in the partial ...