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

Document Type: Full Length Article

Author

University of Tehran, Faculty of Engineering, Department of Engineering Science

Abstract

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

Keywords