Preprint 1997-012

Third Order Nonoscillatory Central Scheme for Hyperbolic Conservation Laws


Abstract: A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: $\#1$. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and $\#2$. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence -- convergent), in the sense that it does not increase the number of initial extrema (--as does the exact entropy solution operator).

Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected third-order resolution.



Paper:
Available as PostScript (2.2 Mbytes) or as gzipped PostScript (0.3 Mbytes; uncompress using gunzip).
Title:
Third Order Nonoscillatory Central Scheme for Hyperbolic Conservation Laws
Author(s):
Xu-Dong Liu, mailto:xliu@cardinal.math.ucsb.edu
Eitan Tadmor, mailto:tadmor@math.ucla.edu
Publishing information:
Numerische Mathematik, to appear
Comments:
Submitted by:
mailto:tadmor@math.ucla.edu April 28 1997.


[ 1996 Preprints | 1997 Preprints | All Preprints | Preprint Server Homepage ]
(c) The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

mailto:conservation@math.ntnu.no
Last modified: Tue Apr 29 12:09:22 1997
Сайт управляется системой uCoz