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Disecretization of 1D advection equation with variable velocities |
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June 15, 2016, 00:29 |
Disecretization of 1D advection equation with variable velocities
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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. |
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advection, disecretization, variable, velocity |
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