Help Required in Discretization - MAC Method

CFDtoy

Hello ,

I have the following equations in a flow with bubbles. f - volume fraction, U velocity, A - area of cross section, p - pressure, rhol - density.

Continuity :

d(f)/dt+ 1/A d(f*A*u)/dx=0

Momentum :

d(f*U)/dt+(1/A)*d(f*U*U*A)/dx=-1\rho * dp/dx

I would like to know, how to solve these 2 equations for U and P . Consider, i have some other correlation for f.

I tried to use the projection method, but I was not able to arrive at a pressure poisson that I would normally get for a divergence free flow.

Can anyone help me with any pseudo language algorithm ?

Thanks

CFDtoy