Add stream line=> uniform density=> Right click=>counter icon => from expression=> select vorticity from turbulent fluid flow turbulent expression

My suggestion is to use Mathematics->PDE Interfaces-> General Form PDE.

For your easier implementation, I suggest the following steps:

1. Solve the first equation only with a constant Omega.

2. Couple the first and the second with a constant or zero theta. For coupling, you do not have to do anything special. Just add two separate physics models by the General Form PDE.

3. Couple all three of them.

You need to have the BCs on the all the boundaries. Also, give suitable ICs for all the variables. Good luck!

Dear Enamul Hasan Rozin.

Your option to use the streamline-vorticity equations instead of the naiver stokes equations in COMSOL cannot work. Instead, make use of Mathematics->PDE Interfaces-> General Form PDE. Always specify your boundary conditions; Solve the primary equation considering omega as a constant; couple the first and the second equation using the general form of PDE; then after couple all the three equations.

Thank you

Dear Sun Kyoung Kim ,

Thank you for your answer. I do not understand what you meant by constant omega in the 1st point and constant or zero theta in your 2nd point. If it is modeled by three different general form PDE physics and three dependent variables in each of the physics and putting all the other portion instead of del.del(dependent variable) in the source term will it suppose to work?

Also there is a boundary condition as in the attached picture in this comment. Can it be modeled by drichlet boundary condition?

I had some confusion. Use the Coefficient Form PDE instead. Fulfilling the first step, you would be familiar with the Coefficient Form PDE by solving a Poisson's equation. Then, in the second step, you will learn how to couple two PDEs. Finally, couple all of them. I think if it is mathematically solvable, it can be solved. In each physics, treat them as a known function of x and y including the mentioned BC.