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 onstaggeredevolution 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 thenumberof initial extrema (--as does the exact entropy solution operator).Extension to systems is carried out by

componentwiseapplication 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, <xliu@cardinal.math.ucsb.edu>
- Eitan Tadmor, <tadmor@math.ucla.edu>
**Publishing information:**- Numerische Mathematik, to appear
**Comments:****Submitted by:**- <tadmor@math.ucla.edu> April 28 1997.

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