Re: [ESPResSo-users] flow profile square duct - deviation

[Ulf Schiller]

Hi Markus,

some deviation from the analytical prediction is of course expected. The
LBM produces a second order approximation of the Navier-Stokes equation,
however, the bounce back boundary conditions implemented in ESPResSo are
only first order accurate. That is, the first thing to double-check is
if you have taken the effective location of the wall correctly into
account - it depends on both the lattice spacing and the relaxation
parameters. What you may meed to do is to tune the eigenvalues of the
ghost modes - not sure whether this is possible from the script level.

What I find intriguing is that you see a spatial variation of the error.
I would have expected that all numerical effects can be accounted for by
an artificial(!) slip velocity, however, it looks like your profile does
not follow a quadratic form. What you can check is how the error
converges, i.e., plot the error vs. the grid spacing. It should decay
linearly or better.

Best wishes,
Ulf

On 20/01/15 14:48, Wink, Markus wrote:
> Hello,
> 
>  
> 
> I used the formula which can be found attached to that email. For the
> series expansion I have used the first 17 entries.
> 
>  
> 
> I have just realized, that I did not really described, what I have done
> in the simulation, sorry about that:
> 
> I simulated a LB-fluid inside a square duct. The fluid consists of
> water, agrid is set to 1. Furthermore a constant force density is
> applied to the fluid nodes.
> 
>  
> 
> Still wondering about the deviation
> 
>  
> 
> Greetings
> 
>  
> 
> Markus
> 
>  
> 
>  
> 
> *Von:*Abdallah Daddi Moussa Ider [mailto:address@hidden
> *Gesendet:* Dienstag, 20. Januar 2015 15:06
> *An:* Wink, Markus
> *Betreff:* Re: [ESPResSo-users] flow profile square duct - deviation
> 
>  
> 
> Dear Markus,
> 
> Did you use the celebrated solution of Spiga and Morini (1994) for your
> comparison? (See the the equations (13)-(17) in this pdf)
> 
> https://lirias.kuleuven.be/bitstream/123456789/288459/1/0673-en.pdf
> 
> bests
> a
> 
>  
> 
>  
> 
> On Tue, Jan 20, 2015 at 11:46 AM, Wink, Markus
> <address@hidden <mailto:address@hidden>>
> wrote:
> 
> Hello everybody,
> 
>  
> 
> I performed a simple simulation of a poiseuille flow in a microfluidic
> square duct. I wanted to check, whether the simulated profile matches
> with the theoretical one (I found the formula in frank M. White’s
> “Viscous Fluid Flow”).
> 
>  
> 
> The simulated values matches the theoretical ones quite good in the
> middle of the channel. Strangely enough, I have a quite big deviation
> close to walls of the channel (the last fluid node closest to the
> boundary nodes), which is even worse in the corners of the channel
> (about 42% deviation (!!) ). I was wondering, where this deviation comes
> from. Attached you will find the simulation script as well as the plots
> showing the deviation.
> 
>  
> 
> Does anyone have a clue, where the deviation comes from?
> 
>  
> 
> Greetings
> 
>  
> 
> Markus
> 
>  
> 
>  
> 
>  
> 


-- 
Dr Ulf D Schiller
Centre for Computational Science
University College London
20 Gordon Street
London WC1H 0AJ
United Kingdom

Phone: +44 (0)20 7679 5300