A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations

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 specific 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.