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

 From: Renard Yves Subject: Re: [Getfem-users] Build a transport equation with the generic procedure Date: Fri, 16 Apr 2010 22:43:40 +0200 User-agent: Dynamic Internet Messaging Program (DIMP) H3 (1.1.2)

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Dear Sebastien,

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The finite element method is instable for the resolution of convection problems. At least without treatment. There is several possible treatments (Petrov-Galerkin, SUPG, additional diffusion term ...). Or you can use another method. A caracteristic Galerkin method is implemented in Getfem, see the command E = gf_compute(mesh_fem MF, vec U, 'convect', mesh_fem mf_v, vec V, scalar dt, int nt[, string option])
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But this is a very dissipative method.

I think your term should be

D = gf.asm_volumic('a=data(mdim(#1),#2); M(#1,#1)+=

with mf_d a scalar fem.

Yves.

sébastien janas <address@hidden> a écrit :

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```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)+=

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

Thanks a lot for your help,

Best regards,

Sébastien Janas

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