Abstract

We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convectiondiffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semi-discrete method in [16]. The method is derived independently of the specific piecewise polynomial reconstruction which is based on the previously computed cell-averages. We demonstrate our results, by focusing on the new third-order CWENO reconstruction presented in [21]. The numerical results we present, show the desired accuracy, high resolution and robustness of our method. Key words. Hyperbolic systems, convection-diffusion equations, central difference schemes, high-order accuracy, non-oscillatory schemes, WENO reconstruction. AMS(MOS) subject classification. Primary 65M10; secondary 65M05.

Citations

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