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Open Access Publications from the University of California

Third-order semi-discrete central scheme for conservation laws and convection-diffusion equations

  • Author(s): Kurganov, Alexander
  • et al.

We present a new third-order, semidiscrete, central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semidiscrete method in [A. Kurgonov and E. Tadmor, J. Comput Phys., 160 (2000) pp. 241-282]. The method is derived independently of the specfic piecewise polynomial reconstruction which is based on the previously computed cell-averages. We demonstrate our results by focusing on the new third-order central weighted essentially nonoscillatory (CWENO) reconstruction presented in [D. Levy, G. Puppo, and G. Russo, SIAM J. Sci. Comput., 21 (1999), pp. 294-322]. The numerical results we present show the desired accuracy, high resolution, and robustness of our method.

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