[Hooman]

I am having problems with the space and time discretization of the Euler equation shown below. I need to use Crank Nicolson for time discretization and 1st or 2nd order upwind for the space discretization. For the purpose of what I'm doing I need to look at a 1D case and that's where I've having the most problems and am not sure about my answers. I believe that I need to ignore the incompressibility condition to begin with as that would get rid of the second term in the equation below and somehow come to the conclusion that that term would become zero after having carried out the discretization...




Any hints suggestion and references would be very much appreciated.