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Boundary condition for fourth order differential equation

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Old   March 23, 2015, 11:26
Default Boundary condition for fourth order differential equation
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Dear Foamers,

actually i am a bit confused of OpenFoam's implementation of boundary conditions.
Actually I have to solve the followong pDGL for my concentration profile:

fvm::ddt(c) == fvm::laplacian(D, "laplacian(c)") (+ other terms)
with D as diffusion coefficient in form of a volScalarField

In this pDGL fourth order derivative with respect to space (and some mixed derivatives) are present, but OpenFoan uses only one boundary condition for the c-Field.
How can this work and is there an easy way to implement the second boundary condition?
Or more detailed: What happens in the fvm::laplacian( ... "laplacian")?
The best way would be to output the CEqn in matrix-form to an external file like the c-Field. Has anybody of you ever done this?

(Btw.: An explicit treatment is already working like A = fvc::laplacian(C) and fvm::ddt(c) == fvc::laplacian(D,A) with seperated BC to c- and A-field.
The question is about the implicit treatment to use Crank-Nicolson in the end and become second order acurate in time.)

Thanks for any comments.
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Old   May 12, 2015, 09:25
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I think, I "solved" the problem on my own.

The matrix structure of OpenFoam (LDU-matrix) does not allow to use the neighbour of a neighbour for discretisation. Only the direct neighbour can be used, so the normal "laplace"-operator is the highest possible implicit derivative.

Therefore a higher implicit derivative is only possible by rewriting all matrix classes and the used solver.
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boundary-conditions, crank-nicolson, fourth order pdgl

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