Commun. Comput. Phys., 2 (2007), pp. 141-163.


On the Reduction of Numerical Dissipation in Central-Upwind Schemes

Alexander Kurganov 1*, Chi-Tien Lin 2

1 Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
2 Department of Applied Mathematics, Providence University, Shalu, 433, Taiwan.

Received 16 December 2005; Accepted (in revised version) 20 July 2006
Available online 30 August 2006

Abstract

We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [13]. Similarly to staggered non-oscillatory central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality and robustness. At the same time, the central-upwind framework allows one to decrease a relatively large amount of numerical dissipation present at the staggered central schemes. In this paper, we present a modification of the one-dimensional fully- and semi-discrete central-upwind schemes, in which the numerical dissipation is reduced even further. The goal is achieved by a more accurate projection of the evolved quantities onto the original grid. In the semi-discrete case, the reduction of dissipation procedure leads to a new, less dissipative numerical flux. We also extend the new semi-discrete scheme to the two-dimensional case via the rigorous, genuinely multidimensional derivation. The new semi-discrete schemes are tested on a number of numerical examples, where one can observe an improved resolution, especially of the contact waves.

AMS subject classifications: 65M10, 65M12, 35L65

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Key words: Hyperbolic systems of conservation laws, Godunov-type finite-volume methods, central-upwind schemes, numerical dissipation.

*Corresponding author.
Email: kurganov@math.tulane.edu (A. Kurganov), ctlin@pu.edu.tw (C. T. Lin)
 

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