In this work, a new formulation for a central scheme recently introduced by A. A. I. Peer et al. is performed. It is based on the staggered grids. For this work, first a time discritization is carried out, followed by the space discritization. Spatial accuracy is obtained using a piecewise cubic polynomial and fourth-order numerical derivatives. Time accuracy is obtained applying a Runge-Kutta(RK) scheme. The scheme proposed in this work has a simpler structure than the central scheme developed in (Peer et al., Appl Numer Math 58 (2008), 674-688). Several standard one-dimensional test cases are used to verify high-order accuracy, nonoscillatory behavior, and good resolution properties for smooth and discontinuous solutions.

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In this work, we present a third-order, semi-discrete, central-upwind scheme for computing approximate solutions of 1D systems of conservation laws. We combine the third-order CWENO reconstruction proposed in Levy et al., the semi-discrete central-upwind numerical flux proposed in Kurganov et al. and the third-order TVD Runge—Kutta method, proposed in Shu and Osher. We are interested in the behavior of the total variation of the approximate solution obtained with this scheme. Also we test our scheme on both scalar and gas dynamics problems. We observe that the total variation of computed solutions is close to the total variation of the exact solution or a reference solution.