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

 May 11, 2005, 05:25 Advection equation.... #1 CFD Question Guest   Posts: n/a Hi all, I have a question regarding a problem I am working on. I have a transport equation for a propogating surface (say the linear advection equation) but the surface moves due to its own propogation speed (say burning velocity) and also due to the flow field velocity. Now, if I write this equation I get d_phi/dt + u d_phi/dx + ub d_phi/dx = 0 where phi is a scalar variable, u is the flow velocity and ub is the burning velocity. Now, assume I am discretizing each term separately (i.e, I am not going to lump the two convective terms together) and if (say) u> 0 and ub< 0 in a 1-D case, then should I use the sum of u+ub to determine the upwind direction for both convective terms (i.e, they have the same upqind direction) or should I use the respective velocity (u or ub) for each term (i.e, they will have different upwind directions in this case? This may seem like a trivial question, but I am not too sure of the answer! Thanks for any help. Any references to books would be appreciated.

 May 11, 2005, 13:42 Re: Advection equation.... #2 Sachin Guest   Posts: n/a Is there a specific reason why you are discretizing each convective term seperately? My first thought is to decide the upwind cell from the sum of u and ub as both of them combined are responsible for effecting the value of phi at a cell.

 May 11, 2005, 17:33 Re: Advection equation.... #3 noName Guest   Posts: n/a Well, before any suggestion, I think it is important to know if u and ub are constants (independant of x). If they are constants, then phi is simply the solution of the wave equation (completely dependant on the initial conditions), traveling at u+ub. If they are not constant, you have yourself a non-linear wave equation which you can solve by various methods (mostly iterative) ...

 May 12, 2005, 05:32 Re: Advection equation.... #4 CFD Question Guest   Posts: n/a u is the velocity field and is solved, so is not independent of x. ub is a function of phi, the scalar variable and therefore we have a non-linear equation. However, it is linearized by making ub dependent on the old time step values. The reason for discretizing the terms separately is numerical (calculating wuth ub inside the Grad phi equation results in problems). So does the fact that one convective term is responsible for moving the wave to the left and the other for moving it to the right (for example) mean that I have a different upwind direction for each or should I use the upwind direction given by u+ub as suggested by Sachin?

 May 12, 2005, 12:00 Re: Advection equation.... #5 noName Guest   Posts: n/a If you linearize the equation to a constant coefficient wave equation, it should not matter whether you discretize the terms separately or combine them. Some easy tests: 1. In the discrete form, can you derive one form from the other by algebriac manipulations? 2. Do they give the same results when computed?

 Thread Tools Display Modes Linear Mode

 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 OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Mihail CFX 7 September 7, 2014 06:27 Sas CFX 15 July 13, 2010 08:56 saii CFX 2 September 18, 2009 08:07 Carolyn Main CFD Forum 6 March 11, 2007 14:21 Mehdi BEN ELHADJ Phoenics 2 April 27, 2001 15:31

All times are GMT -4. The time now is 02:41.