CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

RF-plasma modeling

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

Reply
 
LinkBack Thread Tools Display Modes
Old   July 17, 2001, 09:07
Default RF-plasma modeling
  #1
Tatiana
Guest
 
Posts: n/a
When you try to solve system of electron density and electron energy transport equations coupled with Poisson's equation, using implicit numerical finite-difference scheme, after linearization you obtain ill-conditioned Jacobian matrix ( due to the Poisson's equation). Does anybody know how to deal with this problem?
  Reply With Quote

Old   July 20, 2001, 08:23
Default Re: RF-plasma modeling
  #2
Doug
Guest
 
Posts: n/a
Dear Tatiana,

What do you mean by ill-conditioned? Do you mean that the Gaussian elimination becomes unstable due to lack of diagonal dominance? Or do you simply mean that the problem is stiff and fails to converge?

I've never done plasma simulations using a method involving Poisson's equation - most of the plasma work I've done involves fully coupled solution methods (i.e. simulataneously solving the chemistry and fluid equations in one implicit step) which is more robust for these types of problems.

Another thought - are your conditions close to equilibrium? If so, this can make the equations especially stiff.

If the problem is truly an ill-conditioned matrix, you may want to examine potential ways of changing your formulation - could include upwind differencing, linearlizing using the primitive (rho, u, v,w, P) variables instead of conservative (rho, rho*u, rho*v, total energy,etc.), or underrelaxing the chemistry.

Best wishes with your tackling a challenging problem.
  Reply With Quote

Old   July 20, 2001, 10:20
Default Re: RF-plasma modeling
  #3
Tatiana
Guest
 
Posts: n/a
Dear Doug!

I mean that the Gaussian elimination becomes unstable due to lack of diagonal dominance, and SVD procedure for jacobian gives values of diagonal matrix which differ 10-12 orders of magnitude due to the stiffness. I consider equilibrium conditions in chemistry part. It just gives me the source terms for transport equations.

I was thinking about changing formulation, I substitute expression of electron density from Poisson's equation (ions densities are frozen) through electric potential in electron density transport equation. It leads to five point stencil numerical scheme. But I haven't read before, does anyone do this. I hope it will be usefull.

Thank you for answer.

  Reply With Quote

Old   July 26, 2001, 07:35
Default Re: RF-plasma modeling
  #4
Doug
Guest
 
Posts: n/a
Dear Tatiana,

You truly have an ill-conditioned matrix!!! I don't have any further advice for you beyond what it sounds like you are already doing. Look closely at the individual terms in your Jacobian matrix to identify which terms are the offending ones (probably the chemistry source terms I'd guess). Then modify your formulation (changing the differencing scheme, adding a pseudo-time iteration, implicit smoothing, sub-iterations, etc.) and/or solution alogrithm to improve the behavior.

One thing I've seen done which might enhance stability is to use a first-order upwind LHS (especially using a flux difference or flux vector splitting) with a higher order RHS. This may slow the convergence rate, but such a formulation is generally diagonally dominant. Underrelaxation is another option.

Hope all goes well for you!

Doug

  Reply With Quote

Reply

Thread Tools
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 On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
plasma modeling with CFX eu_eu CFX 6 August 12, 2013 17:39
plasma modeling miroslav1312 FLUENT 3 August 18, 2011 11:28
modeling plasma lucyli FLUENT 0 November 19, 2008 04:14
how to increase temp. in plasma spraying modeling shadi FLUENT 0 August 6, 2007 18:19
Modeling Flow/Saturation/Absorption in Fibers Gene Dougherty Main CFD Forum 0 June 6, 2003 14:49


All times are GMT -4. The time now is 15:30.