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

Looking for low-storage explicit time integration

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

Reply
 
LinkBack Thread Tools Display Modes
Old   February 17, 2005, 04:48
Default Looking for low-storage explicit time integration
  #1
Yves
Guest
 
Posts: n/a
Recently 'Runge-Kutta' has encouraged us on this forum to start using (temporal) error control.

I'm willing to give it a go, but I require some extra properties to be provided by a time integration scheme.

I'm solving hyperbolic equations for aeroacoustics with a DG method, so memory demands are allready high. That's why I also want an explicit, low-storage scheme. Is someone aware of such a scheme?

Currently I'm using the low-storage 6-stage, 4th order RK, optimized for good dispersion and dissipation errors of Berland et al. (AIAA paper 2004-2814).
  Reply With Quote

Old   February 17, 2005, 14:55
Default Re: Looking for low-storage explicit time integrat
  #2
Runge_Kutta
Guest
 
Posts: n/a
There are a few papers on low-storage ERK methods. The topic was very important back in the days of the CRAY XMP-48 but is less so today. Most ERKs were designed thinking the user was not living at the stability boundary. Generally, this is where CFD lives.

http://scholar.google.com/scholar?q=%22low-storage%22+%22runge-Kutta%22&ie=UTF-8&oe=UTF-8&hl=en

Limiting that to ones with embedded methods narrows the field. I think that these do

http://dx.doi.org/10.1016/j.jcp.2004.05.012

http://dx.doi.org/10.1016/S0168-9274(99)00141-5

but there may be some more recent ones. Once you're using a 3(2) or 4(3) pair, you're issue won't be accuracy but will be stability. The trick is to use a method and a controller that can comfortably live at the stability boundary. What you want is a controller that is at least SC-stable on the stability boundary.

http://www.unige.ch/~hairer/books.html

"Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer Series in Comput. Mathematics, Vol. 14, Springer-Verlag 1991, Second revised edition 1996."

If a controller is SC-stable with a method then all real eigenvalues of the governing equations won't bother the controller. Imaginary ones my cause the step size to oscillate a bit from step to step. These constructs are not perfect but will give you some idea of what is going on. Also, since you will likely be very stability bound, your error will be near 10^(-6), or six decimal points of accuracy per step. This means that there is little benefit to methods whose dispersion or dissipation error is small - all temporal error is really small already.
  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
Multiple floating objects CKH OpenFOAM Running, Solving & CFD 12 March 21, 2016 14:05
TimeVaryingMappedFixedValue irishdave OpenFOAM Running, Solving & CFD 28 May 28, 2015 13:37
Upgraded from Karmic Koala 9.10 to Lucid Lynx10.04.3 bookie56 OpenFOAM Installation 8 August 13, 2011 04:03
calculation diverge after continue to run zhajingjing OpenFOAM 0 April 28, 2010 04:35
AMG versus ICCG msrinath80 OpenFOAM Running, Solving & CFD 2 November 7, 2006 16:15


All times are GMT -4. The time now is 15:46.