The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws

Abstract

This work presents two high-order, semi-discrete, central-upwind schemes for<br /> computing approximate solutions of 1D systems of conservation laws. We propose a central<br /> weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order<br /> reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions<br /> with a semi-discrete central-upwind numerical <br /> flux and the third-order TVD Runge-Kutta<br /> method. Also this paper compares the numerical results of these two methods. Afterwards,<br /> we are interested in the behavior of the total variation (TV) of the approximate solution<br /> obtained with these schemes. We test these schemes on both scalar and gas dynamics<br /> problems. Numerical results con rm that the new schemes are non-oscillatory and yield sharp<br /> results when solving profi les with discontinuities. We also observe that the total variation<br /> of computed solutions is close to the total variation of the exact solution or a reference solution.