[EngZara]

hello

i ahve gone through all the turtorials provided by the NUMECA package, I want to edit the PDE in OpenLabs. I want to change the N-S equation into the Vorticity Transport Equation and I am having difficulties with that. if i have a hint on how to implement this, the rest of my problems will be solved
http://brennen.caltech.edu/fluidbook...ytransport.pdf

[colinda1]

Hello,

That is not just slightly editing the PDE but quite a big modification.
To my knowledge this has not been tried before and I would not recommend to use OpenLabs™ for this.
May I ask what would be the reason to solve this vorticity transport equation rather than the NS momentum equation?

To solve as a fluid may not be so obvious for the following reasons:
- how to compute velocity from vorticity in 3D?
- In OpenLabs™ there is no functionality to replace the update of the velocity field (of the internal PDE's) by a dependent field.
- due to preconditioning, it is not possible to split velocity from the coupled NS system.
- how to deduce the pressure from this approach? Would you be interested in the pressure field?

You might consider to solve it as a solid block.
If we forget about pressure, turbulence, numerical robustness... you might try the following:
- use solid block
- define velocity by algebraic expressions
- define PDEs: omega_x, omega_y, omega_z
- define PDEs: psi_yz, psi_zx, psi_xy
steps: Initialize vorticity - solve stream function - solve velocity - solve vorticity

However we don't have confidence on this strategy, as there could be many other issues, like:
- Discretization of the convection term of vorticity PDE's WILL be an issue!
- Need investigations on the boundary conditions of stream function and vorticity PDEs.
- Linear solver for Poisson equation (the stream function) is Gauss-Seidel in OpenLabs, which is not optimal.
- Apply the connections for the PDEs on FNMB (Solid-Solid) if it is multiblock.

Best regards,

Colinda

Head NUMECA Academic Group.

[colinda1]

OpenLabs cannot formulate the Biot-Savart Law. Moreover, as explained in my previous post, we cannot replace the momentum equations. The trick to define vorticity equations in solid block will face discretization problems as described in my previous post as well.