Unaffected Results with Parameter

Hello ,
I am surprised by the results of my 3d model. Its results remain unaffected for all values of parameters used in the model.
[@prj @frederichecht ]
can anyone suggest/comment to resolve it?

Also, an error is popping up for the plot:

"plot: Sorry no ps version for such type of plot 6 "

My code for cubic enclosure with
bottom surface hot,
upper surface cold, and
insulated for all other surfaces in Cubic enclosures are as follows:

cubens.edp (3.2 KB)

The mathematical model is as follows

continuity equation

\frac{\partial U}{\partial X} + \frac{\partial V}{\partial Y} + \frac{\partial W}{\partial Z} = 0

X-directional momentum equation:

\begin{equation} \begin{split} \left( U\frac{\partial U}{\partial X} + V\frac{\partial U}{\partial Y} + W\frac{\partial U}{\partial Z} \right)& = - \frac{\partial P}{\partial X} + Pr\left( \frac{\partial^2 U}{\partial X^2} + \frac{\partial^2 U}{\partial Y^2} + \frac{\partial^2 U}{\partial Z^2} \right) \end{split} \end{equation}

Y-directional momentum eqn

\begin{equation} \begin{split} \left( U\frac{\partial V}{\partial X} + V\frac{\partial V}{\partial Y} + W\frac{\partial V}{\partial Z} \right) =& -\frac{\partial P}{\partial Y} +Pr\left( \frac{\partial^2 V}{\partial X^2} + \frac{\partial^2 V}{\partial Y^2} + \frac{\partial^2 V}{\partial Z^2}\right) \\&- Ha^2 Pr V \end{split} \end{equation}

\begin{equation} \begin{split} \left( U\frac{\partial W}{\partial X} + V\frac{\partial W}{\partial Y} + W\frac{\partial W}{\partial Z} \right) =& -\frac{\rho_{f}}{\rho_{nf}} \frac{\partial P}{\partial Z} + Pr\left( \frac{\partial^2 W}{\partial X^2} + \frac{\partial^2 W}{\partial Y^2} + \frac{\partial^2 W}{\partial Z^2}\right)\\& +RaPr\theta - Ha^2PrW \end{split} \end{equation}

\begin{equation} U\frac{\partial \theta}{\partial X} + V\frac{\partial \theta}{\partial Y} + W\frac{\partial \theta}{\partial Z}= \left( \frac{\partial^2 \theta}{\partial X^2} + \frac{\partial^2 \theta}{\partial Y^2} + \frac{\partial^2 \theta}{\partial Z^2} \right) \end{equation}

I played with this for a while but could not get it t converge as written
or with some modifications. I did question your boundary conditions however.
If this is supposed to be energy and momentum, did you want to set U to
zero at top and bottom? Also you have a cNewton factor on eqn labelled x momentum
which does not look right. I can’t really tell much however since I can’t get it
to converge…

1 Like

Hi @marchywka,
this coupled equation ( momentum and energy) takes care of the continuity equation through the penalty FEM approach.
Also, I have put velocity components zero at each surface due to the no-slip boundary conditions. In my case, it is converging but not affected by the value of the Rayleigh number.

Also, changing boundary conditions show few noticeable changes in the iso-slice of temperature.

Could you please give me a few relevant portals to learn and implement such problems?

Did you try plotting u_z? Fluids isn’t really my thing but apparently the
reynolds number involves the flow velocity and a transition to turbulent
flow. If the veolocity is zero what will happen? You won’t really see much
in any case until you approach a transition AFAICT.
I guess you could try removing the boundariy conditions on u on the top
or bottom or both and see what happens .

Still puzzled why it won’t converge on my fresh clean install…

I have changed the boundary condition and parameter value, which works here:


real Ra= 10^4;

Boundary conditions:

on(1,2,3,4,5,6, u1=0, u2=0, u3=0)
+ on(1, T=sin(pi*y))+ on(3, T=1) ;

======= Results=======

However, could you please comment on identifying the orientation of a mesh as mentioned in [ 3d labels questions]?

It looks like I was just running out ot memory so I changed the elements
to P1 instead of P2. If you plot e3, your boundary conditions on surfaces 5 and 6
create zero flow right? Reomve those and plot u3. With the reynolds number at
1e8 i looks a lot different lol. Not sure any of this is right but if you are modelling
flow along z I’m not sure you cant to set flow to zero at both ends.

I hacked up your code a lot there may be other changes …

1 Like

Thanks, @marchywka for your kind suggestions. Also, I’ll go through it thoroughly.

I have one last doubt, could you please comment on identifying the direction of the axis for a mesh as mentioned in [ 3d labels questions]?