Q-criterion
 

Hi,
could you help me to create a Matlab script for visualization of vortex by Q-criterion? I have the gradient of velocity gained by DNS with software Channelflow. This file because of the construct for becomes 4-D double:
32x33x32x9, where 9 indicates le nine components of the gradient in every nodes.
How can I write the script to display the vortex by the Q-criterion?

Q

where

Ω=tr[ΩΩt ]^1/2and S=tr[SSt ]^1/2

with

S

Let us suppose you have the following matrix:

x(nx,ny,nz): x coordinates of your grid

y(nx,ny,nz): y coordinates of your grid

z(nx,ny,nz): z coordinates of your grid

dudx(nx,ny,nz): x-wise derivative of x-wise velocity component

dudy(nx,ny,nz): y-wise derivative of x-wise velocity component
.
.
.
dwdz(nx,ny,nz): z-wise derivative of z-wise velocity component

This is, more or less, how i would put it down in Matlab:

%MATLAB CODE

iso_q=100; %Pick your number here

%Definition of Q
q=-0.5*(dudx.^2+dvdy.^2+dwdz.^2)-dudy.*dvdx-dudz.*dwdx-dvdz.*dwdy;

%Plotting a Q isosurface, Q=iso_q
figure()
p=patch(isosurface(x,y,z,q,iso_q));
set(p,'FaceColor','red','EdgeColor','none');
daspect([1,1,1])
axis tight
ax = -1; ay = 1; az = 1;
view([ax,ay,az]);
camroll(240)
camlight
lighting gouraud

%END OF MATLAB CODE

hope it works

Thanks a lot... ;)

sbaffini

Can you please write a blog with all this cool stuff (and also for LES)

Dear Far,

i'm glad you appreciate my contributions. I admit that is now a long time i'm thinking about putting all this stuff together in some place that i already identified as a cfd-online blog...

However, as you may imagine, time is never enough as all the material would require some modifications or testing before being directly posted for the general use. In contrast, posting specific answers once in a while is more easy and directly useful for the one who asked.

Nonetheless, as my working group was also considering this opportunity to "share stuff", i promise i will now seriously consider posting on a blog.

It took me a while to actually understand what you meant by blog. I'm doing it now ;)

;) I am still trying to understand :D

@sbaffini: You have wonderful skills

Still, they are quite difficult to exchange with money ;)

Thanks

uits for Q-criterion
 

I have a simple question what units are used for q-criterion

You leave out the important stuff here: the calculation of the velocity gradients, which is not difficult, but needs care

Nevermind my answer, i read incorrectly

Dimensions are velocity squared over length squared, which is inverse time squared.