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modify fvMatrix / coupled equations / higher order diffusion

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Old   May 7, 2011, 06:20
Default modify fvMatrix / coupled equations / higher order diffusion
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Jinming Lu
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Dear OpenFOAM community,

I've just started using OpenFOAM, trying to solve an equation of the type

df/dt = laplacian(laplacian(f))

for higher order diffusion

To my limited knowledge (please correct if I am wrong), simple diffusion

df/dt = laplacian(f) is already implemented and
Code:
fvScalarMatrix fEqn
(
    fvm::ddt(f) - fvm::laplacian(f)
);
creates an equation of the type (for the implicit case)

(F - F0)*V/deltaT - A*F

where F is a vector/list containing the cell values of f to be calculated, F0 those of the previous time step, V is the volume, deltaT is the time step, and A denotes the "discretized laplacian" (coefficient matrix).

A naive solution of

df/dt = laplacian(laplacian(f))

would be creating an equation of the type

(F - F0)*V/deltaT - A*A*F,

i.e. multiplying the fvMatrix A obtained from fvm::laplacian(f) by itself.

I would be grateful if someone could give me a hint on the implementation or how to solve the coupled problem

df/dt == laplacian(g)
laplacian(f) == g

Thanks in advance.

Best regards,

Jinming
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