I just came across Total Variation Diminishing schemes, where it has been mentioned that for the scheme to be non-oscillating, the following criteria should be followed:
- the scheme should be monotonic preserving i.e.
- it must not create local extreme
- the value of an existing local minimum must be non-decreasing, and that of a local maximum must be non-increasing.
May someone elaborate or explain, how these are not obeyed on QUICK or Central difference (as these are only conditional TVD).
In addition to Sweby's paper, you might also want to look at Berger, Aftosmis, and Murman's paper on slope limiters, which gives an excellent, different perspective on the limiters available for making a scheme TVD.
http://people.nas.nasa.gov/~aftosmis/publications/aiaa2005_0490.pdf
- Badges
- Science topic