A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws

  • Authors:

  • A. A. I. Peer;A. Gopaul;M. Z. Dauhoo;M. Bhuruth

  • Affiliations:

  • Department of Mathematics, University of Mauritius, Reduit, Mauritius;Department of Mathematics, University of Mauritius, Reduit, Mauritius;Department of Mathematics, University of Mauritius, Reduit, Mauritius;Department of Mathematics, University of Mauritius, Reduit, Mauritius

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2008

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Abstract

We propose a new fourth-order non-oscillatory central scheme for computing approximate solutions of hyperbolic conservation laws. A piecewise cubic polynomial is used for the spatial reconstruction and for the numerical derivatives we choose genuinely fourth-order accurate non-oscillatory approximations. The solution is advanced in time using natural continuous extension of Runge-Kutta methods. Numerical tests on both scalar and gas dynamics problems confirm that the new scheme is non-oscillatory and yields sharp results when solving profiles with discontinuities. Experiments on non-linear Burgers' equation indicate that our scheme is superior to existing fourth-order central schemes in the sense that the total variation of the computed solutions are closer to the total variation of the exact solution.