## Nonoscillatory Central Schemes For Multidimensional Hyperbolic Conservation Laws (1998)

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Venue: | SIAM J. Sci. Comput |

Citations: | 80 - 14 self |

### BibTeX

@ARTICLE{Jiang98nonoscillatorycentral,

author = {Guang-shan Jiang and Eitan Tadmor},

title = {Nonoscillatory Central Schemes For Multidimensional Hyperbolic Conservation Laws},

journal = {SIAM J. Sci. Comput},

year = {1998},

volume = {19},

pages = {1892--1917}

}

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### Abstract

We construct, analyze, and implement a new nonoscillatory high-resolution scheme for two-dimensional hyperbolic conservation laws. The scheme is a predictor-corrector method which consists of two steps: starting with given cell averages, we first predict pointvalues which are based on nonoscillatory piecewise-linear reconstructions from the given cell averages; at the second corrector step, we use staggered averaging, together with the predicted midvalues, to realize the evolution of these averages. This results in a second-order, nonoscillatory central scheme, a natural extension of the one-dimensional second-order central scheme of Nessyahu and Tadmor [J. Comput. Phys., 87 (1990), pp. 408--448]. As in the one-dimensional case, the main feature of our two-dimensional scheme is simplicity. In particular, this central scheme does not require the intricate and time-consuming (approximate) Riemann solvers which are essential for the high-resolution upwind schemes; in fact, even the com...