How do i model convection in a liquid?

I am hoping to write a computer program to model a column of water with different conditions at the top and bottom (exposed to weather at the top, and either cooled or not cooled at the bottom). My goal is to figure out when it will freeze over based on different conditions.

My plan is to chop this vertical column up into individual cells and every hour change the conditions at the top and bottom, and then calculate the changes in each cell for the new hour.

So simulate convection, I was thinking I would just sort the cells by density after calculating each cell's temperature.

Obviously this wouldn't be super accurate because if two cells need to swap position because of changes in density, there will be substantial mixing as they change position.

But I don't need this simulation to be super accurate. But I also don't want it to be completely unreasonable.

So keeping in mind how simplistic my model is, how would you add in convection while still keeping the model simplistic.

And just to be clear, this is a 1 dimensional model.

Thanks for any pointers.