Uniform Weighted Compact and Non-Compact Scheme for Shock Entropy Interaction

Peng Xie and Chaoqun Liu ()
Additional contact information
Peng Xie: University of Texas at Arlington, Department of Mathematics
Chaoqun Liu: University of Texas at Arlington, Department of Mathematics

A chapter in Computational Mechanics, 2007, pp 257-257 from Springer

Abstract: Abstract A new type of high order shock capturing schemes - uniform weighted compact and non-compact scheme (UWCNC) is developed in this work. This new scheme is based on the feature of discrete data set. The data are first normalized and then measured by so called “smoothness”. The strategy of this new scheme is to achieve spectral-like resolution and high order of accuracy by using central weighted compact scheme in smooth and oscillatory regions and use the non-compact scheme to cross the shock to capture shocks sharply without oscillation. In a 6th order one parameter family of the compact schemes (Lele, 1992), we turn the control parameter to 1/3, keeping the exact formulation of the 6th order weighted compact scheme and turn it to zero gradually when approaching the shock, which makes the scheme non-compact. Besides the WENO (Jiang et al, 1996) weights, there is only one additional control parameter, which we call smoothness function. In this new uniform weighted compact-non compact scheme, a sixth-order weighted compact scheme and a corresponding fourth-order weighted non-compact scheme are combined following this basic idea. Numerical tests show that the new scheme has captured the 1-D shock sharply without non-physical oscillation and obtained much higher resolution for 1-D shock-entropy interaction than the 5th order WENO scheme.

Keywords: Parameter Family; Exact Formulation; Finite Difference Scheme; Discrete Data; WENO Scheme (search for similar items in EconPapers)
Date: 2007
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75999-7_57

Ordering information: This item can be ordered from
http://www.springer.com/9783540759997

DOI: 10.1007/978-3-540-75999-7_57

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().