Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??

[Wink, Markus]

Hi Ulf,

Some mails ago you wrote: 
> You could check that the convergence is O(Ma^2).

Why should the convergence be O(Ma^2)? Could you be so kind and explain it to 
me?  It is not clear for me.

Thanks,

Markus

-----Ursprüngliche Nachricht-----
Von: Ulf Schiller [mailto:address@hidden 
Gesendet: Montag, 21. März 2016 12:17
An: Wink, Markus; address@hidden
Cc: 'Georg Rempfer'; Joost de Graaf
Betreff: Re: AW: [ESPResSo-users] No conservation of momentum/mass in LBM ??

Hi,

On 03/21/2016 12:05 PM, Wink, Markus wrote:
> Hello everybody,
> 
>  
> 
> by „reduce the force density” I guess you mean the velocity of the 
> rhomboids. I did that, and indeed, the extents of in- and outlet 
> effects are almost equal. So I guess, that I have some compressibility 
> artefacts in my system, which gets more pronounced if the velocity of 
> the rhomboids increase. So I was thinking, that it might be related to 
> the mach number. But looking at the mach number in the script I was 
> attaching some mails ago, it is of the order of  1E-3 (if I am not 
> mistaken). So compressibility effects shouldn’t play any role.
> 
>  
> 
> Still puzzling…

You could check that the convergence is O(Ma^2).

Cheers,
Ulf

> *Von:address@hidden [mailto:address@hidden *Im 
> Auftrag von *Georg Rempfer
> *Gesendet:* Freitag, 18. März 2016 10:19
> *An:* Wink, Markus
> *Cc:* Joost de Graaf; address@hidden; Ulf Schiller
> *Betreff:* Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??
> 
>  
> 
> I think it's possible that the asymmetry stems from the fact that at 
> one boundary, there is a density discontinuity and on the other one, 
> there is not.
> 
>  
> 
> Can you reduce the force density and rerun? I think that will reduce 
> the density gradient and therefore the discontinuity at one end.
> 
>  
> 
> I might be completely wrong about this.
> 
>  
> 
> On Fri, Mar 18, 2016 at 9:11 AM, Wink, Markus 
> <address@hidden <mailto:address@hidden>>
> wrote:
> 
> Hello everybody,
> 
>  
> 
> the mass flux is constant in the system. Makes sense ... Thanks a lot!
> 
>  
> 
> The only question that is left for me now is, why the entry and outlet 
> are not symmetric. Actually I am not sure anymore, if they should be 
> symmetric. The system does not exhibit a mirror symmetry, so my 
> assumption of having symmetric in- and outlet effects might not be 
> valid (but I am not sure about it).
> 
>  
> 
> Any ideas about it? Notice, that although the graph implies the in- 
> and outlet have different velocities, I set the velocities of the 
> rhomboids at both sides to same velocities.
> 
>  
> 
> Greetings
> 
>  
> 
> Markus
> 
>  
> 
>  
> 
>  
> 
> *Von:*Joost de Graaf [mailto:address@hidden 
> <mailto:address@hidden>]
> *Gesendet:* Donnerstag, 17. März 2016 16:58
> *An:* Georg Rempfer
> *Cc:* Wink, Markus; address@hidden 
> <mailto:address@hidden>; Ulf Schiller
> 
> 
> *Betreff:* Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??
> 
>  
> 
> Georg is right. Done that once for a sphere, it worked out perfectly 
> back then.
> 
>  
> 
> On 17 March 2016 at 15:55, Georg Rempfer <address@hidden 
> <mailto:address@hidden>> wrote:
> 
> If the density goes up along the channel, the velocity has to go down 
> to fulfill mass conservation.
> 
>  
> 
> Since there are density variations in the system, you should check the 
> actual mass flux instead of the averaged velocity. That means you 
> should integrate density*velocity over every slice and look at the 
> component normal to the slice.
> 
>  
> 
> On Thu, Mar 17, 2016 at 10:33 AM, Wink, Markus 
> <address@hidden <mailto:address@hidden>>
> 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.
> 
> 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?
> 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?
> 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).
> 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).
> 6) Have anyone ever checked the second order accuracy of the LBM in 
> ESPResSo?
> 
> Greetings and thanks a lot for your help!
> 
> Markus
> 
> 
> 
> 
> -----Ursprüngliche Nachricht-----
> Von: address@hidden
> <mailto:address@hidden>
> [mailto:espressomd-users-bounces+markus.wink
> <mailto:espressomd-users-bounces%2Bmarkus.wink>address@hidden
> nu.org <mailto:address@hidden>] Im Auftrag von Ulf 
> Schiller
> Gesendet: Mittwoch, 16. März 2016 13:49
> An: address@hidden <mailto: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>
> <mailto: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
> g
> <mailto:address@hidden>
>>     <mailto:address@hidden
> <mailto:address@hidden>>
>>     [mailto:espressomd-users-bounces+markus.wink
> <mailto:espressomd-users-bounces%2Bmarkus.wink>
>>     <mailto:espressomd-users-bounces%2Bmarkus.wink
> <mailto:espressomd-users-bounces%252Bmarkus.wink>>address@hidden
> ongnu.org
> <mailto:address@hidden>
>>     <mailto: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> 
> <mailto: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>
> <mailto: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>
>>     <mailto:address@hidden
> <mailto:address@hidden>>>
>>     > Date: 3/15/2016 8:47 AM (GMT-05:00)
>>     > To: 'Ivan Cimrak' <address@hidden <mailto:address@hidden>
> <mailto:address@hidden <mailto:address@hidden>>>,
>>     address@hidden <mailto:address@hidden>
> <mailto: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
> g
> <mailto:address@hidden>
>>     <mailto:address@hidden
> <mailto:address@hidden>>
>>     > [mailto:espressomd-users-bounces+markus.wink
> <mailto:espressomd-users-bounces%2Bmarkus.wink>
>>     <mailto:espressomd-users-bounces%2Bmarkus.wink
> <mailto:espressomd-users-bounces%252Bmarkus.wink>>address@hidden
> ongnu.org
> <mailto:address@hidden>
>>     <mailto:address@hidden
> <mailto:address@hidden>>] *Im Auftrag von *Ivan Cimrak
>>     > *Gesendet:* Dienstag, 15. März 2016 13:22
>>     > *An:* address@hidden
> <mailto:address@hidden> 
> <mailto: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 <tel:1-864-656-2669>
> Fax: 1-864-656-5973 <tel: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