Cahn-Hilliard equation: Difference between revisions

Revision as of 02:09, 7 February 2020

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In this example we will show how to solve the Cahn-Hilliard equation in Medusa. The solution provides an implementation of periodic boundary conditions and shows how to combine implicit and explicit operators. This example uses a custom biharmonic operator, so we recommend firstly reading the tutorial on Customization.

Cahn-Hilliard equation

The Cahn-Hilliard equation describes the separation of binary fluid into pure domains. We define concentration, a scalar field $c(x, y) \in [-1, 1]$ to describe the fluid, with values $c \pm 1$ representing pure phases. In this case the equation can be written as

\[ \frac{\partial c}{\partial t} = D \nabla^2 (c^3 - c - \gamma \nabla^2 c), \] where $D$ is the diffusion constant and $\sqrt{\gamma}$ is the characteristic transition length between domains.

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-In this example we will show how to solve the [https://en.wikipedia.org/wiki/Cahn%E2%80%93Hilliard_equation Cahn-Hilliard] equation in Medusa. The solution provides an implementation of periodic boundary conditions and shows how to combine implicit and explicit operators. This example uses a custom biharmonic operator, so we recommend firstly reading tutorial on [[Customization]].
+In this example we will show how to solve the [https://en.wikipedia.org/wiki/Cahn%E2%80%93Hilliard_equation Cahn-Hilliard] equation in Medusa. The solution provides an implementation of periodic boundary conditions and shows how to combine implicit and explicit operators. This example uses a custom biharmonic operator, so we recommend firstly reading the tutorial on [[Customization]].
 == Cahn-Hilliard equation ==