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 ziemowitzima January 28, 2013 12:50

nonlinear equation with non-constant (nonlinear) and direction dependent diffusion

Dear Foamers,

I am trying to solve/implement nonlinear equation with non-constant (nonlinear) and direction dependent diffusion.
It looks like that:

Equation is solved for in rectangular domain:

I decided to solve it as follows:

fvScalarMatrix yEqn
(
fvm::ddt(y)
- U.component(1)
- fvm::laplacian(nu + (A/C)*nu2, y)
+ D/C
);

where:
nu and nu2 are defined to act in z and u directions respectively
nu = (1 0 0 0 0 0 0 0 0) and nu2 = (0 0 0 0 1 0 0 0 0 0),
and

and

and
, (vertical velocity)
where A, C and D are solved explicitly.
But solver had a problem with it, because C were getting too large.

So I decided to multiply above equation by C and get:

fvScalarMatrix yEqn
(
C*fvm::ddt(y)
- C*U.component(1)
- fvm::laplacian(C*nu + A*nu2, y)
+ D
);

Here I got solution, somehow similar to the one it should converge, but not exactly.
Problem seems to be in "C*fvm::ddt(y)" term, because it gives me the same answer if I have just "fvm::ddt(y)" ...

Any idea, what can be here wrong, or how to make it better ?

Thanks
ZMM

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