streamfunction-vorticity
 

Dear all,

I want to develop a simple streamfunction-vorticity code operating in a rectangular domain (chanel).

If you have experience with such things, in particular with inflow/outflow boundary conditions please share your knowledge with me.

If you have experience in general with inflow/outflow boundary conditions, please also share your knowledge with me.

many thanks,

Christophe

Re: streamfunction-vorticity
 

(1). Since it is a channel flow, the outflow condition can be used at the exit, that is zero gradient of all variables. The first order method would be VARI(i=imax,j)=VARI(i=imax-1,j) for j=1 to jmax (1). (2).For the inlet conditions, you can specify the velocity profile (uniform or non-uniform), and calculate the vorticity and streamfunction based on the definition there. (by differentiation and integration).

Re: streamfunction-vorticity
 

Hello John,

thank you for your help. I have heard that zero gradient is only a very basic method, that why you call it first order?

In fact it is not quite a channel flow I am doing. I will use FFT in the cross-streamwise direction, so it is a two-pi periodic domain along this one.

In the streamwise direction I will use finite differences just because I want to have an open domain problem, this is the point of my modelling effort.

I know all variables at the inlet, but I have read that one usually does not specify all variables there, rather one variable is left to fluctuate and is computed self-consistently from the numerical scheme being used.

Christophe

Re: streamfunction-vorticity
 

(1). The downstream condition I mentioned is first order, because you can also use three-point formula to get the same zero gradient condition. So, it is first order two point formula. (2). In stream function-vorticity formulation, you have two variables and two governing equations, therefore, you have to specify both the stream function and the vorticity there. The same is true for the downstream condition. The velocity in this case is just the intermediate variable. It is always derived from the current stream function. (3). I guess you are free to do your own experiments in setting the boundary conditions. It is only my suggestion.