AFT Arrow solves all of the fundamental controlling equations governing gas dynamics. For more information about which fundamental thermodynamic equations are solved in AFT Arrow, here is an excellent article that discusses gas flow calculations in detail.  

The "stack effect" is simply one aspect of these equations, and is accounted for by the user input and boundary conditions. Ultimately, flow is driven by pressure difference. The higher you raise a chimney, the lower the atmospheric density and pressure at the discharge.

In order to accurately model the "stack effect", the system boundary conditions must be modeled accurately.  As the discharge elevation of a chimney increases, then the system boundary pressure condition at the top of the stack must decrease accordingly.  The figure below illustrates the stack effect quite well in regards to what the pressures would look like at different elevations.  

Stack Effect with Text

As you can see in the above image, there are two columns of air.  The left column of air is at atmospheric conditions.  The lower elevation at the bottom of the air column has a higher pressure than the higher elevation point of the air column.

The pressure at the top of the chimney stack is the same as the atmosperic pressure at the same high elevation point in the column of air.

This pressure difference of the atmospheric air column needs to be accounted for in the model in order to accurately model the stack effect.  The best way to model the stack effect in AFT Arrow would be with using three assigned pressure junctions.

The below image illustrates an example of how one might model the stack effect in AFT Arrow.  The assigned pressure junction on the left would be specified with the ambient atmospheric pressure conditions (pressure, temperature, and elevation).  The connecting pipe can be short and perhaps frictionless or hydraulically smooth to minimize the pressure drop.  The assigned pressure junction on the right would have the pressure and temperature (and elevation) of the process at the base of the stack.  Or, the rest of the process system can tie into the stack at this location.

Stack Effect Arrow 5

Finally, the assigned pressure junction at the top of the stack would be specified at atmospheric conditions at the higher elevation point (pressure, temperature, and elevation).  At this point, the atmospheric pressure will be lower than the atmospheric pressure at the elevation of the bottom of the stack.

Fundamentally, the pressure at the top of the stack needs to be lower than the atmospheric pressure and process pressure at the bottom of the stack in order to drive the flow up the stack.  By defining these boundary conditions properly, the density differences will be accounted for properly for the stack effect.