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New High-Resolution Central-Upwind Schemes for Nonlinear Hyperbolic Conservation Laws

In: Hyperbolic Problems: Theory, Numerics, Applications

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  • Chi-Tien Lin

    (Providence University, Department of Applied Mathematics)

Abstract

The main feature of central schemes is that they are Riemann-solver free. The original high-order central scheme by Nessyahu and Tadmor [NeTa] assumes a global speed of wave propagation which introduces a large amount of numerical viscosity and lowers the resolution of discontinuities. Later, Kurganov and Tadmor [KurTa] proposed a new version of central schemes. In their construction, the whole space is divided into smooth and singular rectangular controlled volumes according to local speed of wave propagation. The updated values at each gridpoints are obtained from more precise computation on each region resulting in sharper resolution and less numericiil viscosity. In this paper, we shall construct new fully-discrete central-upwind scheme by replacing the rectangular singular regions with smaller triangular regions. Numerical simulation will be present to show lower numerical viscosity and hence sharper results, as expected.

Suggested Citation

  • Chi-Tien Lin, 2003. "New High-Resolution Central-Upwind Schemes for Nonlinear Hyperbolic Conservation Laws," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 705-715, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_66
    DOI: 10.1007/978-3-642-55711-8_66
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