Ok, thanks very much, I will keep you informed.
Quinta-feira, 23 de Maio de 2013 15:42:31 UTC+1, Robert Cimrman escreveu:
On 05/23/2013 04:31 PM, dj....@gmx.de javascript: wrote:
Just to inform you. Actually I tried to find out what error could lead to non-solving the 3 eqn I had before.
Therefore I just used your navier_stokes.py script with a different mesh, the mesh I also use for my equations and the definitions of the regions and boundary conditions. With the 3d_elbow mesh it worked fine but using the cube_big_tetra.mesh I get the same error like in my script, umfpack out of memory.
Could the reason be somewhere in the mesh/region/boundary condition defintion?
The elbow.mesh is much smaller than cube_big_tetra.mesh. But it no that big either (you said you have 4GB, right?), so there seems to be something fishy with the linear system matrix. In my experience, the more is the matrix ill-conditioned (towards being almost singular), the more memory umfpack needs.
You can verify the regions and boundary conditions definitions using:
./simple.py <file> --save-ebc --save-ebc-nodes --save-regions-as-groups
and then view the resulting files with postproc.py (mayavi2), or in paraview.
r.
Quinta-feira, 23 de Maio de 2013 15:26:20 UTC+1, Robert Cimrman escreveu:
On 05/23/2013 04:12 PM, dj....@gmx.de javascript: wrote:
Yes, exactly, if we consider incompressiblity in a homogeneous case
then
both will be uncoupled. That´s what of course works fine to model. But I really want the coupled case. So if I use your proposition, the last equation:
Laplace(V) + (grad(V)/grad(h)) * Laplace (h) = 0
How would I implement it in sfepy? Because this is one equation but 2 unknown variables. I can only use one test variable. Is it possible to solve?
Well, we still have a missing equation. Otherwise the above equation could be implemented for example using a solution-dependent material coefficient, as in [1].
r.
[1]
http://sfepy.org/doc-devel/examples/diffusion/poisson_field_dependent_materi...
Quinta-feira, 23 de Maio de 2013 15:00:53 UTC+1, Robert Cimrman
On 05/23/2013 03:29 PM, dj....@gmx.de javascript: wrote:
Ok, the complete equations are basically those, from which I derived
escreveu: the
simplified ones:
- j=-sigma * grad(V) - L * grad(h)
- div j = 0
- u= -k/eta * grad (h)
- L/sigma=grad(V)/grad(h)
With L, sigma, k, eta constant as this is a homogeneous case. Also
it
stationary. h is the hydraulic potential (scalar) and V the Self-Potential (scalar) , u is the velocity vector. When I apply eq. 2) on eq. 1) I get the following:
- sigma * Laplace(V) + L * Laplace (h) = 0
This can be modelled with dw_laplace.
Eq. 4) I tried with the dw_stokes but as you are right I thought it takes the gradient, so I will try your proposittion with dw_v_dot_grad_s. If considering a divergence-free velocity field, we could add div u
0, the incompressibilty,which will lead to a modified eq. 3)
3*) -k/eta * Laplace (h) = 0
Well, then 5) reduces to sigma * Laplace(V) = 0, which certainly can be solved, but I am not sure it is what you want :) - there is no coupling at all.
But I actually didn´t want this case because I tried to add a source (a well) into the middle of the cube. Anyway, for testing purpose we could try to use this. So are eqn. 4), 5), 3*) correct and can they be the 3 eqn. needed to model? Or should I use div u = 0 instead of 3*)?
I know nothing about this problem, so all I can provide are negative statements ("this will not work") - I do not know what is the right weak
3*) means that V and h are solutions to Laplace equations and are decoupled. Then I do not know, if/how 4) could be enforced. Is it that L, sigma actually depend on the solution, so that 5) could be written as this:
Laplace(V) + (L / sigma) * Laplace (h) = 0
so
Laplace(V) + (grad(V)/grad(h)) * Laplace (h) = 0
- is grad(h) always nonzero?
r.
Thanks for your help!
Quinta-feira, 23 de Maio de 2013 12:44:56 UTC+1, Robert Cimrman escreveu: > > I think we first need to get the equations right. > > > 1) sigma * Laplace(V) + L * Laplace (h) = 0 > > 2) L/sigma * grad(h) - grad(V) = 0 > > - the 2) uses grad(h), grad(V), but you use dw_stokes, which corresponds > to > \int div(h) q, \int \div{V} q (and thus has a scalar test
function).
Look
> at > dw_v_dot_grad_s instead(?) > > Do you have the complete equations written somewhere? Maybe you are > over-simplifying something here. > > It seems to me, that you have: > - scalar unknown hydraulic head h > - scalar unknown self_Potential signal V > - velocity vector v > > So there should be three equations, two of them multiplied by a scalar > test > functions corresponding to h and V, and one multiplied by a vector test > function, corresponding to v. > > r. > > On 05/23/2013 12:48 PM, dj....@gmx.de javascript: wrote: >> Thanks Robert, >> when I try now the corrected equations (scalar test variable q for
is formulation. the
>> first equation, vectortest variable s for the second) and introduce a > third >> equation (simplified Navier Stokes without stokes term, with a vector > test >> variable uv) I get the following memory error: >> >>
failed with >> UMFPACK_ERROR_out_of_memory >> >> Both vector test variables are related to the same field (velocity). I >> might not have understood the formulation of the weak eqn.correctly. >> >> 'Head-SP' : >> """dw_laplace.i3.Omega( fluid.sigma, q, v ) + dw_laplace.i3.Omega( >> fluid.C_sigma_rel, q, h ) = 0""", >> 'Coupling-Coef' : >> """dw_stokes.i3.Omega( fluid.C_sigma_rel, s, h ) - > dw_stokes.i3.Omega( >> s, v ) = 0""", >> 'Navier-Stokes' : >> """dw_div_grad.i3.Omega( fluid.dyn_viscosity, uv , u ) + >> dw_convect.i3.Omega( uv , u ) = 0""", >> >> I'm using linux fedora as a virtual box in windows 7 system, allowing > 4GB >> of RAM for linux. >> >> Sorry for all this, just need this step and then I hope I will get it. >> Thanks again, >> Djamil >> >> Quarta-feira, 22 de Maio de 2013 16:33:25 UTC+1, Robert Cimrman > escreveu: >>> >>> Hi Djamil, >>> >>> On 05/22/2013 04:16 PM, dj....@gmx.de javascript: wrote: >>>> Dear friends, >>>> I'm trying to solve the following *equations *for the self-potential >>>> distribution along a water injection in a well. >>>> >>>> 1) sigma * Laplace(V) + L * Laplace (h) = 0 >>>> 2) L/sigma * grad(h) - grad(V) = 0 >>> >>> The weak form of your equations below seems to be wrong - as grad(h) > and >>> grad(V) are vectors, the second equation has to be tested by a vector > test >>> variable. Then this vector test variable should have a corresponding >>> unknown >>> vector variable (the velocity) - there should be IMHO one more equation >>> with that. >>> >>> Also, each one of the above equations should be tested by a single test >>> variable - you are mixing it in the equations. >>> >>>> *Here h is the hydraulic head (pressure) distribution, V is the >>>> Self_Potential signal*. >>>> I'm using the *3d_cube_big_tetra mesh*. The code is attached. >>>> >>>> The *boundary conditions* are: >>>> Left and right side of the cube h=100m >>>> Left side of the cube (reference point) V=0mV. >>>> Center cells of the cube: h=1000m (injection of water) >>>> >>>> In general it should be very easy to find a solution with sfepy FE but > I >>>> don´t get any relation between V and h, although both should be > coupled >>> via >>>> the L/sigma parameter. L and sigma are constant in this *homogeneous >>> case*(L=-1.5e-7, sigma=1). >>>> >>>> Hydraulic head (h) is calculated correctly, but the SP signal (V) > shows >>> no >>>> connection to h. Changing the parameters L or sigma has absolutely no >>>> effect on the solution. It depends only on the boundary conditions. >>>> >>>> So I tried to implement it with the following *equations*: >>>> * >>>> 1 'SP' : >>>> """dw_laplace.i3.Omega( fluid.sigma, w, v ) + > dw_laplace.i3.Omega( >>>> fluid.C_sigma_rel, q, h ) = 0""", >>>> 2 'Coupling' : >>>> """dw_stokes.i3.Omega( fluid.C_sigma_rel, q, h ) - >>> dw_stokes.i3.Omega( >>>> w, v ) = 0""", * >>>> >>>> A probe image through the middle of the cube is attached. >>>> >>>> So my questions: >>>> >>>> 1) Am I using the right equations? I also tried it with dw_div_grad >>> instead >>>> of dw_laplace (should be the same, no?) but unfortunately the >>> calculation >>>> then doesn't converge. >>> >>> Use dw_div_grad for vector variables, and dw_laplace for scalar > variables. >>> >>>> 2) Why is the coupling between both Laplacian eqn. not given? There >>> should >>>> be an effect of L and sigma even without defining eqn 2 (Coupling) but >>> it >>>> has no effect. This is not a SP problem but more a general issue > because >>>> there should be a coupling between both unless one part is zero. >>> >>> I guess this is caused by the one equation that is IMHO missing... >>> >>>> That's why I'm afraid that having problems already with a homegeneous >>> case >>>> leads to much more problems with inhomogeneous sigma and L >>> distributions. >>>> >>>> Thanks very much for any hints and suggestions. I'm really out of > ideas >>> now. >>> >>> I some more observations/suggestions related to the example file: >>> >>> - in field_2, use 'shape' : 'vector' instead of 'shape' : (2,), - that >>> will >>> work for both 2D and 3D meshes >>> - it does not run with current sfepy (fmf_sumLevelsMulF(): ERR_BadMatch > (4 >>> == >>> 12, 1 == 1, 1 == 1)) - this is caused by using the scalar test > functions >>> in the >>> second equation >>> - when I correct the test field of the second equation to be "s" > (vector), >>> the >>> system assembles, but the matrix is singular, as there is no "u" in the >>> equations.