ziemowitzima 
January 28, 2013 12:50 
nonlinear equation with nonconstant (nonlinear) and direction dependent diffusion
Dear Foamers,
I am trying to solve/implement nonlinear equation with nonconstant (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
