CFD Online Logo CFD Online URL
Home > Forums > General Forums > Main CFD Forum

Stability for Nonlinear Numerical Scheme

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

LinkBack Thread Tools Display Modes
Old   February 1, 2001, 13:34
Default Stability for Nonlinear Numerical Scheme
Posts: n/a
It is usual for the application of Von Neumann or matrix methods in the stability analysis of a numerical scheme for a linear PDE. But Neuman method can only be used for linear problems. For nonlinear problem, for example Du/Dt = -(1/2)D(uu)/Dx - 32 (Du/Dx)^2+D^2u/Dx^2, Neuman method can not be used. How do we do the stability analysis for this kind of nonliear PDE after disretization, or where can I get reference materials on this issue?

Thank you!
  Reply With Quote

Old   February 6, 2001, 10:59
Default Re: Stability for Nonlinear Numerical Scheme
Patrick Godon
Posts: n/a
If you write the discretized non-linear equation assuming a first order perturbation


you can linearize the equation (after the discretization).

WOuld that help you ?

  Reply With Quote

Old   February 7, 2001, 12:51
Default Re: Stability for Nonlinear Numerical Scheme
Ralf Massjung
Posts: n/a
This problem was addressed by Poinsot and Candel for the inviscid Burgers-Equation in Journal of Computational Physics, vol. 62, 282-296, 1986.
  Reply With Quote

Old   February 12, 2001, 13:21
Default Re: Stability for Nonlinear Numerical Scheme
clifford bradford
Posts: n/a
Culbert Laney discussed this in great detail in Chapters 15 and 16 of his book Computational Gasdynamics. In fact the linear stability is still relevant.
  Reply With Quote


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
Numerical viscosity due to the MUSCL and HLL coulpled scheme sonsiest Main CFD Forum 0 May 23, 2011 15:37
How to implement a numerical scheme by using UDF? Furui Xiong FLUENT 0 July 29, 2010 01:30
problem about numerical scheme in LES. libin Main CFD Forum 4 July 1, 2004 04:32
the numerical scheme for LES. John S Main CFD Forum 2 March 14, 2004 08:52
numerical scheme ado Main CFD Forum 3 October 12, 2000 08:20

All times are GMT -4. The time now is 16:30.