Hi,

As per John’s suggestion, I’m emailing it to the
whole users list for some very simple questions on example 13:

·
We are solving the gov. equations for a lid
driven cavity in 2D:

rho*(v_i,0 + v_i,j*v_j) + p_i -
mu*v_i_jj = 0

v_ii = 0

The FEM formulation of the above
equations in example 13 is not clear to me. Can anyone help?

Boundary conditions are implemented
using penalty method.

I couldn’t figure out the
exact formulation to figure how it’s doing it.

(I’m not very knowledgeable
about FEM and trying to relate what I read in a book e.g. for say linearized
burger’s equation v_i,0 + vbar_j*v_i,j – nu*v_i,jj – f_i =
0 with generalized galerkin methods leads to the formulation (A +
dt/2*(B+K)*V^n+1 = [A-dt/2*9B+K)]v^n + dt*(F + G)). (A is mass matrix, K
is stiffness matrix etc.

Now this is basically in the form
A*u =B . which is then solved for u. The formulation is DST approximation.

So basically how does the ex13
implementation translates to something like above.

The book I’m referring is
Computational Fluid Dynamics by T J Chung.

I’m pretty sure it’s
quite simple and those who have done it can quickly scribble. I might be able
to figure it out eventually as I get proficient in FEM but it would save me a
lot of time if you folks can help me here.

·
The above should hopefully also answer how we
have a terms like Kuu, Kup , Kuv etc. which are themselves matrices.

·
I wanted to compute Re of the flow but couldn’t
find the value of “nu” used in the problem? (L & u is 1
but don’t know nu, 1/300 ??)

Any help would be greatly appreciated. Unless I understand
all this I’m finding it difficult to move on.

Regards,

Anurag