Space and time discretization of Euler equation
 

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...

http://upload.wikimedia.org/math/8/c...df9c879184.png


Any hints suggestion and references would be very much appreciated.

You could have a look at the Wiki / Reference Section / Numerical Methods as a starting point. A next step could to get a decent book on numerical methods for CFD. That should get you started.

Thanks,
I need to use collocated grid arrangments and Rhie Chow interpolation for the pressure and velocity coupling. I don't really understand the Rhie chow interpolation and what the steps are in applying that.

Do I first discretize the pressure and diffusion terms in space using the Rhie Chow interpolation method and then discretize the whole equation in time using the Crank-Nicolson interpolation method?

Aslo is the Rhie-Chow interpolation method used along with an algorithm such as the Simple Algorithm?

Thank you in advance.