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?

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 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_material.html

>
>
> Quinta-feira, 23 de Maio de 2013 15:00:53 UTC+1, Robert Cimrman escreveu:
>>
>> On 05/23/2013 03:29 PM, dj....@gmx.de <javascript:> wrote:
>>> Ok, the complete equations are basically those, from which I derived the
>>> simplified ones:
>>>
>>> 1) j=-sigma * grad(V) - L * grad(h)
>>> 2) div j = 0
>>> 3) u= -k/eta * grad (h)
>>> 4) L/sigma=grad(V)/grad(h)
>>>
>>> With L, sigma, k, eta constant as this is a homogeneous case. Also it is
>>> 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:
>>>
>>> 5) 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 formulation.
>>
>> 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 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:
>>>>>
>>>>> <function umfpack_di_numeric at 0x2dbac08> 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.
>>
>>
>