CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > System Analysis

Disecretization of 1D advection equation with variable velocities

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   June 15, 2016, 00:29
Default Disecretization of 1D advection equation with variable velocities
  #1
New Member
 
Join Date: Jun 2016
Posts: 1
Rep Power: 0
funlandhuman is on a distinguished road
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.
funlandhuman is offline   Reply With Quote

Reply

Tags
advection, disecretization, variable, velocity

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Solving Transport equation for additional variable using CFX creddy_trddc CFX 11 April 2, 2015 22:07
Diffusion Advection equation discretization scheme Farouk Main CFD Forum 0 July 2, 2013 17:10
additional variable in diffusion-trasnport equation mva CFX 5 June 21, 2013 04:42
emag beta feature: charge density charlotte CFX 4 March 22, 2011 10:14
2D linear advection equation mcaro Main CFD Forum 2 February 11, 2011 13:30


All times are GMT -4. The time now is 20:26.