[Getfem-users] Build a transport equation with the generic procedure

[sébastien janas]

Hi,

I try to solve a transport equation with getfem.

I have problem to deal with the term

div (  RHO * Y * U )

where

- div is the divergence
- RHO is the density
- Y is a moisture content
- U is the velocity

I try to build the matrix

(PSI_x^i * RHO * U_x * PSI^j ) + 
(PSI_y^i * RHO * U_y * PSI^j ) +
(PSI_z^i * RHO * U_z * PSI^j )

where - PSI_a^b are the derivative of the base functions at nodes b in
respect to ditection a

      - PSI^b are the base functions at nodes b 

      - U_a are the a components of velocity

In my program, I have the product RHO*U in a (nb_dof x 3) array, and I
construct my matrix like this

D = gf.asm_volumic('a=data(#2); M(#1,#1)+=
sym(comp(Grad(#1).Base(#1).Base(#1))(:,i,:,k).a(i,k))',mim,mf_u,mf_d,DATA)

where mf_u is 

mf_u  = gf.MeshFem(m,1)
mf_u.set_fem(gf.Fem("FEM_PK(3,1)"))

and mf_d

mf_d  = gf.MeshFem(m,3)
md_d.set_fem(gf.Fem("FEM_PK(3,1)"

My questions are these

-> Is it the correct way to solve a transport equation ?
-> Is anybody have an exemple of such equation ?
-> With the exemple above, I get the following error that I don't
understand, is there somebody who can explain it to me ?

 "wrong number of indexes for the 2th argument of the reduction
comp(Grad(#1).Base(#1).Base(#1))(:,i,:,k).a(i,k) (ranges=[0..12])"

Thanks a lot for your help,

Best regards,

Sébastien Janas