A Predictor-Corrector Scheme for Conservation Equations with Discontinuous Coefficients

Nasrin Okhovati (Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, 7635131167)
Mohammad Izadi (Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, 7616913439)

Journal of Mathematical and Fundamental Sciences
Vol. 52 No. 3 (2020)

In this paper we propose an explicit predictor-corrector finite difference scheme to numerically solve one-dimensional conservation laws with discontinuous flux function appearing in various physical model problems, such as traffic flow and two-phase flow in porous media. The proposed method is based on the second-order MacCormack finite difference scheme and the solution is obtained by correcting first-order schemes. It is shown that the order of convergence is quadratic in the grid spacing for uniform grids when applied to problems with discontinuity. To illustrate some properties of the proposed scheme, numerical results applied to linear as well as non-linear problems are presented.