[funlandhuman]

I am currently working on a project involving two-phase flow through pipes and I am required to model it in MatLab. Even though I have started and get some pertinent results I get the feeling that something is not right and I think it might be the way I was solving the advection equations.
The equation I am trying to solve is



d(Hl x rhoL)/dt + d(Hl x rhoL x Vl)/dx = 0

where: Hl=liquid fraction;

rhoL= liquid density;

Vl=liquid velocity;


The liquid being incompressible I do not take in account the density as it is constant.


I am trying to solve this equation for the liquid velocity at time t+dt (velocity is not constant).


What I have done so far is consider Hl=U and Hl x Vl= V and using a forward difference in time and backward difference in space I ended up with the following formula:

Vl(i,1)=(((Hlold(i,1)-Hl(i,1))*(deltaX/deltaT))+(Vl(i-1,1)*Hl(i-1,1)))/Hl(i,1));

Do you guys think this is correct? Can someone help me understand how I can disecretize the PDE having variale velocities through the nodes?

Thanks a lot guys and sorry if I have not posted in the right thread. I am new to this forum.