On the total variation of a third-order semi-discrete central scheme for 1D conservation laws

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.