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Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??
From: |
Ulf Schiller |
Subject: |
Re: [ESPResSo-users] No conservation of momentum/mass in LBM ?? |
Date: |
Thu, 17 Mar 2016 11:08:21 -0400 |
User-agent: |
Mozilla/5.0 (X11; Linux i686; rv:38.0) Gecko/20100101 Thunderbird/38.1.0 |
On 03/17/2016 10:51 AM, Wink, Markus wrote:
> Hello everybody,
>
>> Your plot suggests that the inlet velocity is different from the outlet
>> velocity. In that case it makes sense that the boundary effects have a
>> different extent.
>
> Sorry for the misleading picture. The first and last data point should of
> cause be the velocity of the rhomboid. I set both rhomboids with the same
> velocity (see tcl-script attached). So the boundary effects should have same
> extent, which they clearly don't have. Could this also be related to a
> slightly compressed fluid?
>
>> In LB, as you say, the pressure is proportional to the density, so you could
>> set the density at the outlet. This is in fact what the Zhou/He boundary
>> condition effectively does.
>
> Is it really that simple? I mean, for the outlet we have 5 unknown
> distribution functions (the ones having a velocity vector pointing inwards to
> the channel). If I set a certain density at the outlet, I only have one
> equation for those 5 unknown distributions. I could also imply a normal
> output boundary condition for the flow, so setting u_y and u_z to zero. This
> gives me another two relations. As far as I know, Zou/He assume furthermore,
> that for the non-equilibrium part of the distribution function there is a
> bounce-back rule, giving the last two relations needed to solve the system of
> equations.
> I am just wondering, if it is promising to just set the density at the outlet
> to a certain value (maybe in combination with normal output condition for the
> velocity) to get rid of the output effects. Any idea/feeling about it?
Of course Zhou/He would be cleaner, but you'd need to implement that
(which is not difficult). Just setting the density will not satisfy the
normal and non-equilibrium conditions (which will affect the stress
tensor, but you have an artificial profile anyhow). I'm not sure what
will happen, but may be worth a quick'n'dirty try...
Cheers,
Ulf
> -----Ursprüngliche Nachricht-----
> Von: Ulf Schiller [mailto:address@hidden
> Gesendet: Donnerstag, 17. März 2016 14:30
> An: Wink, Markus; address@hidden
> Betreff: Re: AW: [ESPResSo-users] No conservation of momentum/mass in LBM ??
>
> Hi Markus,
>
> On 03/17/2016 05:33 AM, Wink, Markus wrote:
>> Hello everybody,
>>
>> I checked the mass flux. It is constant over the length of the channel (some
>> oscillations at the outlet, but I am not concerned about it). I revised the
>> script and now I get the maximum velocity right (less than 1% deviation to
>> the theoretical one). But I am still puzzling with some aspects. First of
>> all I checked whether the density is constant. Within one plane
>> perpendicular to the direction of flow, that is the case. Along the
>> direction of transport, I notice a drop of the density. This makes sense to
>> me, since the density is proportional to the pressure and I expect a linear
>> pressure profile along the channel.
>
> Well, in principle the density should be constant in an incompressible fluid.
> Now, since you are adding momentum to the system through the inlet velocity,
> I think the fluid is locally compressed at the inlet, so a (small) density
> gradient may develop. So I think your observation makes sense. However, if
> the density gradient becomes too large, it may lead to instabilities.
>
>> Nevertheless, there are some questions left.
>>
>> 1) I have noticed, that in both cases, whether if I apply a body force to
>> the fluid or an constant velocity inlet boundary condition, the maximum
>> velocity of the profile is a bit lower than the expected one (although it is
>> quite good with less than 1% deviation). I am just wondering, since I
>> checked two "methods", whether this deviation lies in the nature of the LBM
>> algorithm?
>
> I would say 1% is a pretty good agreement. You could check that you get the
> expected convergence by reducing the grid size (see below).
>
>> 3) With a constant velocity inlet and constant velocity outlet I have inlet
>> and outlet effects of cause a certain length (until the profile develops). I
>> was expecting that the two lengths should be equal, since I have equivalent
>> boundary conditions. In the appendix you will see, that this is not the case
>> (it shows the velocity as a function of the x-position, while y- and z- are
>> set to half the channel width/height). The entry effect seems to be much
>> more pronounced, but I am not sure why. Does anyone have an idea?
>
> Your plot suggests that the inlet velocity is different from the outlet
> velocity. In that case it makes sense that the boundary effects have a
> different extent.
>
>> 4) As an outlet condition it would be neat to have a constant pressure
>> boundary condition (with that, one would eliminate the outlet effect). I was
>> thinking to put the outlet-nodes to a constant pressure via lbnode set. Is
>> there a command for setting the pressure of a node to a given value
>> (investigating the source code it seems, that there is only "lbnode x y z
>> print pi" but not set).
>
> In LB, as you say, the pressure is proportional to the density, so you could
> set the density at the outlet. This is in fact what the Zhou/He boundary
> condition effectively does.
>
>> 5) What is the proper way to get the mean velocity out of the mass flux? If
>> I sum up the velocities and divide by the cross section, I get a slight
>> increase of v_mean along the channel (I have no idea why).
>
> This could be related to the different velocities at the inlet and the
> outlet. The mass flux should be constant far away from the boundaries though.
>
>> 6) Have anyone ever checked the second order accuracy of the LBM in
>> ESPResSo?
>
> I did that a long time ago, and would support the idea of adding a
> corresponding test case. However, many of the LB features in ESPResSo,
> including the integrator, are only first order accurate (either in time or
> space).
>
> Hope this helps.
>
> Best wishes,
> Ulf
>
>> -----Ursprüngliche Nachricht-----
>> Von: address@hidden
>> [mailto:address@hidden
>> org] Im Auftrag von Ulf Schiller
>> Gesendet: Mittwoch, 16. März 2016 13:49
>> An: address@hidden
>> Betreff: Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??
>>
>> Hi Markus,
>>
>> sorry for the confusion. In my earlier email I should have said mass flux of
>> course, i.e., the Q in the formulas Kai provided. You can calculate that
>> from the simulated velocity profile for each plane along the channel, and it
>> should be constant.
>>
>> Best,
>> Ulf
>>
>> On 03/16/2016 08:21 AM, Georg Rempfer wrote:
>>> Assuming the fluid is not compressed (you could check that, but it's
>>> likely true), the mass flux is proportional to the velocity. You
>>> claim the average velocity in the channel direction is too low half
>>> way between inlet and outlet. This implies that mass gets lost
>>> between the inlet/outlet and the middle (or that the lb fluid is
>>> denser in the middle). Can you check that?
>>>
>>> On Wed, Mar 16, 2016 at 1:02 PM, Wink, Markus
>>> <address@hidden
>>> <mailto:address@hidden>>
>>> wrote:
>>>
>>> Hello everybody,____
>>>
>>> __ __
>>>
>>> thank you for your answers. I did not get it. Which quantity is of
>>> interest? Mass flux or momentum flux? I am not sure about it,
>>> although to check whether mass conservation is fulfilled, both
>>> should work, am I right?____
>>>
>>> __ __
>>>
>>> __ __
>>>
>>> Greetings____
>>>
>>> __ __
>>>
>>> Markus____
>>>
>>> ____
>>>
>>> __ __
>>>
>>> __ __
>>>
>>> *Von:address@hidden
>>> <mailto:address@hidden>
>>> [mailto:espressomd-users-bounces+markus.wink
>>> <mailto:espressomd-users-bounces%2Bmarkus.wink>address@hidden
>>> <mailto:address@hidden>] *Im Auftrag von *Georg Rempfer
>>> *Gesendet:* Mittwoch, 16. März 2016 11:26
>>> *An:* Kai Szuttor
>>> *Cc:* address@hidden <mailto:address@hidden>
>>> *Betreff:* Re: [ESPResSo-users] No conservation of momentum/mass in
>>> LBM ??____
>>>
>>> __ __
>>>
>>> I agree with you argument, Markus. Mass conservation dictates that
>>> the normal flow through every surface along the channel should be
>>> the same (assuming the flow is incompressible). Together with the
>>> fixed shape of the fully developed flow profile, this uniquely
>>> determines the flow in regions far away from the inlet/outlet. So if
>>> this does not come out correctly, mass conservation should be broken
>>> somewhere. I don't think this is possible in the LB. Can you
>>> calculate this flux through the surfaces along the channel and show
>>> us where exactly it differs from the inlet/outlet?____
>>>
>>> __ __
>>>
>>> On Tue, Mar 15, 2016 at 5:09 PM, Kai Szuttor
>>> <address@hidden <mailto:address@hidden>>
>>> wrote:____
>>>
>>> Now with attachment :)
>>>
>>> Am 15/03/16 um 14:07 schrieb Ulf D Schiller:
>>> > Did you check the flow rates directly, i.e., the momentum flux per
>>> plane? Your argument seems correct, so I can only guess that there's
>>> some
>>> > flaw in the calculation of the mean velocity. I think there's an
>>> expression for the flux in rectangular channels that one could use.
>>> >
>>> > Best,
>>> > Ulf
>>> >
>>> > Sent from a mobile device.
>>> >
>>> >
>>> > -------- Original message --------
>>> > From: "Wink, Markus" <address@hidden
>>> <mailto:address@hidden>>
>>> > Date: 3/15/2016 8:47 AM (GMT-05:00)
>>> > To: 'Ivan Cimrak' <address@hidden <mailto:address@hidden>>,
>>> address@hidden <mailto:address@hidden>
>>> > Subject: Re: [ESPResSo-users] No conservation of momentum/mass in
>>> LBM ??
>>> >
>>> > Hi Ivan, Hi Florian,
>>> >
>>> >
>>> >
>>> >>/How did you compute the expected maximum velocity? As far as I
>>> know, the poisseuille flow has an exact expression for the velocity
>>> in the case
>>> > of channel with circular cross section, and you have a rectangular
>>> one.///
>>> >
>>> > / /
>>> >
>>> > I know the velocity of the rhomboid. Thus I know the mean velocity
>>> of the fluid (assuming it is incompressible). I took that for
>>> calculating the
>>> > Reynoldsnumber, pressure gradient and theoretical velocity profile
>>> (using the expression in the book “Viscous Fluid Flow” of Frank M.
>>> White).
>>> >
>>> >
>>> >
>>> > /> //The boundaries are momentum sinks. (Florian)/
>>> >
>>> > /> Now I read the comment of Florian -//does that mean that amount
>>> of fluid is decreasing when no-slip is prescribed?/
>>> >
>>> > I still don’t get it. That the boundaries are momentum sinks, I
>>> agree. Due to the present of the walls and the “friction” of the
>>> fluid there, I
>>> > achieve the poiseuille profile. But I still hold the opinion, that
>>> the mean velocity of the fluid should be the same.
>>> > Imagine the following physical experiment: you have a syringe pump
>>> set up with a constant flow rate Q0 connected to a rectangular
>>> channel having
>>> > a cross section A=w*h. The fluid in the channel then has a mean
>>> velocity of v_mean=Q/A. Assuming an incompressible medium, this
>>> means the
>>> > velocity should be the same at every slice normal the direction of
>>> transport.
>>> > In my simulation, the mean velocity should be velocity v0 of the
>>> rhomboid.
>>> >
>>> > So I still don’t get the deviation to the theoretical value…
>>> >
>>> > Greetings Markus
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>> *Von:address@hidden
>>> <mailto:address@hidden>
>>> > [mailto:espressomd-users-bounces+markus.wink
>>> <mailto:espressomd-users-bounces%2Bmarkus.wink>address@hidden
>>> <mailto:address@hidden>] *Im Auftrag von *Ivan Cimrak
>>> > *Gesendet:* Dienstag, 15. März 2016 13:22
>>> > *An:* address@hidden <mailto:address@hidden>
>>> > *Betreff:* Re: [ESPResSo-users] No conservation of momentum/mass
>>> in LBM ??____
>>>
>>> >
>>> >
>>> >
>>> > Hi Markus,
>>> >
>>> >
>>> >
>>> > Hello Everybody,
>>> >
>>> >
>>> >
>>> > so far, in the LBM scheme only the body force is implemented
>>> and no velocity/pressure boundary condition. So I was thinking on a
>>> way of
>>> > mimicking a “velocity boundary” condition without changing the
>>> source code. I am aware that one should, as a proper approach, using
>>> Zou/He
>>> > boundary conditions and adjusting the distribution functions
>>> according to the boundary conditions.
>>> >
>>> >
>>> >
>>> > For that I have constructed a channel with rectangular cross
>>> section and put the fluid inside. Furthermore, two rhomboids where
>>> put inside,
>>> > one at the inlet of the channel, one at the outlet. The cross
>>> section of the two rhomboids is equal to the cross section of the
>>> channel,
>>> > furthermore they have a constant velocity v0.
>>> >
>>> > My idea was, that, since the no-slip boundary condition is
>>> implemented, I force the fluid nodes adjacent to the rhomboids to
>>> have a constant
>>> > velocity, thus achieving constant velocity inlet/outlet condition.
>>> >
>>> >
>>> >
>>> > As a result I achieve a poiseuille profile in the middle of
>>> the channel (fully developed flow after inlet/outlet effects). The
>>> qualitative
>>> > pressure gradient looks proper, too.
>>> >
>>> > Nevertheless, the maximum velocity is not the same as I
>>> expected (factor 3 to the expected one).
>>> >
>>> > How did you compute the expected maximum velocity? As far as I
>>> know, the poisseuille flow has an exact expression for the velocity
>>> in the case
>>> > of channel with circular cross section, and you have a rectangular
>>> one.
>>> >
>>> >
>>> > I have checked the mean velocity. I would expect, that the mean
>>> velocity of the fluid should be the velocity v0 of the rhomboid (due to
>>> > mass/momentum conservation), I get less (10 %).
>>> >
>>> > This is strange. The amount of fluid at the inlet (integral of
>>> velocity over the inlet surface, in this case is the velocity
>>> constant over the
>>> > inlet surface) should be the same as integral over the middle
>>> cross section, as well as integral over the outlet surface....
>>> Supposing you
>>> > computed the average velocity as sum of velocities over the LB
>>> nodes at middle cross section divided by number of these nodes, you
>>> should have
>>> > obtained the velocity at the inlet...
>>> >
>>> > Now I read the comment of Florian - does that mean that amount of
>>> fluid is decreasing when no-slip is prescribed?
>>> >
>>> > Ivan
>>> >
>>> >
>>> >
>>> > What is wrong with my idea stated here? Obviously, something is
>>> not correct, but I have no idea, what the reason for that is. Where
>>> does the
>>> > momentum vanish?
>>> >
>>> >
>>> >
>>> > Does anybody have an idea?
>>> >
>>> >
>>> >
>>> > Sincerely,
>>> >
>>> >
>>> >
>>> > Markus
>>> >
>>> >
>>> >
>>> >
>>> >____
>>>
>>> __ __
>>>
>>>
>>
>>
>> --
>> Dr. Ulf D. Schiller
>> Assistant Professor
>> Department of Materials Science and Engineering Clemson University
>> 161 Sirrine Hall
>> Clemson, SC 29634
>>
>> Office: 299c Sirrine Hall
>> Phone: 1-864-656-2669
>> Fax: 1-864-656-5973
>>
>
>
> --
> Dr. Ulf D. Schiller
> Assistant Professor
> Department of Materials Science and Engineering Clemson University
> 161 Sirrine Hall
> Clemson, SC 29634
>
> Office: 299c Sirrine Hall
> Phone: 1-864-656-2669
> Fax: 1-864-656-5973
>
--
Dr. Ulf D. Schiller
Assistant Professor
Department of Materials Science and Engineering
Clemson University
161 Sirrine Hall
Clemson, SC 29634
Office: 299c Sirrine Hall
Phone: 1-864-656-2669
Fax: 1-864-656-5973
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, (continued)
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf D Schiller, 2016/03/15
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Kai Szuttor, 2016/03/15
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Kai Szuttor, 2016/03/15
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Georg Rempfer, 2016/03/16
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/16
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Georg Rempfer, 2016/03/16
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf Schiller, 2016/03/16
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf Schiller, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??,
Ulf Schiller <=
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Georg Rempfer, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Joost de Graaf, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/18
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Georg Rempfer, 2016/03/18
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/21
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf Schiller, 2016/03/21
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf Schiller, 2016/03/18