Calculation of Vorticity

mortain · July 8, 2010, 18:49

Hello,

I am using fortran for simulating the fluid flow not based on Navier Stokes but on lattice Boltzmann method!

I would like to evaluate the vorticity, given the velocity vectors.

The vorticity is, for the x direction, equal to:

_x=(u_z(x,y+1,z)-u_z(x,y,z))-(u_z(x,y,z+1)-u_z(x,y,z))
since

u/

x=lim(

x-->0)[u(x+

x)-u(x)]/

x hence I have to take the value of the next lattice minus the value at the lattice divided by one, which is the

x.

Apparently tihs doesn't give the expected result in terms of vorticity. I was reading something here: http://folk.uio.no/jks/matpiv/html/node31.html but I'm not sure and I wanted the opinions of CFD, since in CFD softwares the vorticity is evaluated automatically.

Regards

Antonio

Rami · July 12, 2010, 04:10

The vorticity definition (in tensor notation) is wik = (ui,k-uk,i)/2, while your expression is wx=ux,y-uz,z - which is wrong.

July 8, 2010, 18:49	Calculation of Vorticity	#1
mortain New Member Antonio Join Date: Sep 2009 Posts: 12 Rep Power: 16	Hello, I am using fortran for simulating the fluid flow not based on Navier Stokes but on lattice Boltzmann method! I would like to evaluate the vorticity, given the velocity vectors. The vorticity is, for the x direction, equal to: _x=(u_z(x,y+1,z)-u_z(x,y,z))-(u_z(x,y,z+1)-u_z(x,y,z)) since u/x=lim(x-->0)[u(x+x)-u(x)]/x hence I have to take the value of the next lattice minus the value at the lattice divided by one, which is the x. Apparently tihs doesn't give the expected result in terms of vorticity. I was reading something here: http://folk.uio.no/jks/matpiv/html/node31.html but I'm not sure and I wanted the opinions of CFD, since in CFD softwares the vorticity is evaluated automatically. Regards Antonio

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July 12, 2010, 04:10		#2
Rami Senior Member Rami Ben-Zvi Join Date: Mar 2009 Posts: 155 Rep Power: 17	The vorticity definition (in tensor notation) is wik = (ui,k-uk,i)/2, while your expression is wx=ux,y-uz,z - which is wrong.