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

Osher's Scheme

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

LinkBack Thread Tools Search this Thread Display Modes
Old   September 14, 2008, 09:26
Default Osher's Scheme
Posts: n/a
Why does Osher use eigenvector decomposition to integrate instead of using the vectors itself for integrating?
  Reply With Quote

Old   September 16, 2008, 08:13
Default Re: Osher's Scheme
Posts: n/a
i'm writing directly from the following paper, pages 68-69

"J.Casper, H.L.Atkins, A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems, Journal of Computational Physics, 106, 62-76"

"(...) It would therefore seem natural, purely from the viewpoint of approximation theory, to reconstruct the set {u_ij} by applying the scalar reconstruction R^2 in a component-wise fashion. However, this approach is valid only if we assume that u(x,y,t) remains free of discontinuities for the duration of a desired calculation. But in the more general case, when u(x,y,t) is a solution of a non-linearly coupled system of equations, such a solution can admit the collision of discontinuites of the same or of different families, as well as their collision with boundaries, i.e. solid walls. In the vicinity of such collisions, a component-wise reconstruction may develop spurious oscillations during this brief encounter which do not dissipate as the discontinuites then distance themselves from one another, if indeed they ever do. (...) It is argued in [6] that, in the constant-coefficient case, it is adventageous to use these characteristic variables in the reconstruction procedure, rather than u itself. This is do to the fact that, under the transformation, the coupled system becomes an independent set of equations, thereby rendering any discontinuity in a particular characteristic variable -undetectable- by another."

hope this helps
  Reply With Quote


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
Implementation of QUICK scheme Romuald Skoda Main CFD Forum 11 November 6, 2017 21:20
AUSM scheme ? Central Scheme boling Main CFD Forum 7 January 7, 2016 02:41
2nd order upwind scheme (Fluent and CFX) Far FLUENT 0 May 22, 2011 01:50
how to understand high resolution scheme and high order scheme iilw1314 Main CFD Forum 3 September 30, 2010 10:43
extrapolation in MUSCL scheme Chandra Main CFD Forum 6 February 14, 2007 11:21

All times are GMT -4. The time now is 02:07.