Implement Q-criterion

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As nicely shown in invariant2_factor.m
in https://github.com/Tianshu-Liu/OpenOpticalFlow

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https://de.mathworks.com/matlabcentral/answers/1566758-find-q-criterion-and-lambda2-from-velocity-values?s_tid=srchtitle

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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 the task of plotting Q isosurfaces (tipically used for flow visualization in DNS/LES):

%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

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#!MC 1400

Created by Tecplot 360 build 14.0.2.35002

$!ALTERDATA
EQUATION = '{Q} = 0'

$!VarSet |NUMVARSINIT| = |NUMVARS|
$!VarSet |NUMVARSINIT| += 1

$!PROMPTFORTEXTSTRING |U|
INSTRUCTIONS = "Enter the variable number for U"
$!PROMPTFORTEXTSTRING |V|
INSTRUCTIONS = "Enter the variable number for V"
$!PROMPTFORTEXTSTRING |W|
INSTRUCTIONS = "Enter the variable number for W"

$!GLOBALTHREEDVECTOR UVAR = |U|
$!GLOBALTHREEDVECTOR VVAR = |V|
$!GLOBALTHREEDVECTOR WVAR = |W|

$!ALTERDATA
EQUATION = '{dudx} = ddx(u)'
$!ALTERDATA
EQUATION = '{dvdx} = ddx(v)'
$!ALTERDATA
EQUATION = '{dwdx} = ddx(w)'
$!ALTERDATA
EQUATION = '{dudy} = ddy(u)'
$!ALTERDATA
EQUATION = '{dvdy} = ddy(v)'
$!ALTERDATA
EQUATION = '{dwdy} = ddy(w)'
$!ALTERDATA
EQUATION = '{dudz} = ddz(u)'
$!ALTERDATA
EQUATION = '{dvdz} = ddz(v)'
$!ALTERDATA
EQUATION = '{dwdz} = ddz(w)'
$!ALTERDATA
EQUATION = '{s11} = {dudx}'
$!ALTERDATA
EQUATION = '{s12} = 0.5*({dudy}+{dvdx})'
$!ALTERDATA
EQUATION = '{s13} = 0.5*({dudz}+{dwdx})'
$!ALTERDATA
EQUATION = '{s22} = {dvdy}'
$!ALTERDATA
EQUATION = '{s23} = 0.5*({dvdz}+{dwdy})'
$!ALTERDATA
EQUATION = '{s33} = {dwdz}'
$!ALTERDATA
EQUATION = '{Omga12} = 0.5*({dudy}-{dvdx})'
$!ALTERDATA
EQUATION = '{Omga13} = 0.5*({dudz}-{dwdx})'
$!ALTERDATA
EQUATION = '{Omga23} = 0.5*({dvdz}-{dwdy})'
$!ALTERDATA
EQUATION = '{s2o2_11} = {s11}**2 + {s12}**2 + {s13}**2 - {Omga12}**2 - {Omga13}**2'
$!ALTERDATA
EQUATION = '{s2o2_12} = {s11}{s12} + {s12}{s22} + {s13}{s23} - {Omga13}{Omga23}'
$!ALTERDATA
EQUATION = '{s2o2_13} = {s11}{s13} + {s12}{s23} + {s13}{s33} - {Omga12}{Omga23}'
$!ALTERDATA
EQUATION = '{s2o2_22} = {s12}**2 + {s22}**2 + {s23}**2 - {Omga12}**2 - {Omga23}**2'
$!ALTERDATA
EQUATION = '{s2o2_23} = {s12}{s13} + {s22}{s23} + {s23}{s33} - {Omga12}{Omga13}'
$!ALTERDATA
EQUATION = '{s2o2_33} = {s13}**2 + {s23}**2 + {s33}**2 - {Omga13}**2 - {Omga23}*2'
$!ALTERDATA
EQUATION = '{Q} = 2{Omga12}*2 + 2{Omga13}*2 + 2{Omga23}**2 - {S11}**2 - {S22}**2 - {S33}*2 - 2{S12}*2 - 2{S13}*2 - 2{S23}**2'

$!VarSet |NUMVARSFIN| = |NUMVARS|
$!DELETEVARS [|NUMVARSINIT|-|NUMVARS|]