http://mathsci.ucd.ie/~plynch/eniac/CFvN-1950.pdf
It's something you can solve in a few lines of python and run with minimal compute resources. A nice thing to try is to feed in some data from somewhere like below and watch what happens as you integrate it forwards in time.
http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalys...