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Cahn Hilliard implementation (Biharmonic operator)

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Old   February 15, 2016, 03:36
Default Cahn Hilliard implementation (Biharmonic operator)
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Joe Peterson
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I'm interested in modeling viscoelastic phase separations in simple flows. As a first step in the process, I want to implement a simple diffusive phase separation such as the Cahn Hilliard equation using OpenFOAM.

There are at least several threads with people asking for advice for solving the Cahn Hilliard equation, and as of last active discourse (~2012) there was no publicly distributed resolution to the main problem (an implicit treatment of the fourth order derivative in the problem)

A link to one of the prior threads on this topic:

The grand challenge is that, for a stable implementation, a fourth order spatial derivative (the biharmonic operator) must be calculated implicitly at some stage. One common way to accomplish this is to solve simultaneously for two variables such that the model assumes the following structure:

x = laplacian(y)
dx/dt = laplacian(x + y)

I'm new to the environment, but so far it seems that in OpenFOAM the solver only solves a single field at a time; can I trick it into solving for these two variables simultaneously? Is there another way that I should be thinking about the problem?

Any help or insight into this challenge would be greatly appreciated!
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biharmonic, cahn hilliard, phase field, phase separations

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