The third-order relaxation schemes for hyperbolic conservation laws

Authors:
Xiang-Gui Li;Xi-Jun Yu;Guang-Nan Chen
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong;Institute of Applied Physics and Computational Mathematics, Beijing, People's Republic of China;Institute of Applied Physics and Computational Mathematics, Beijing, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

A class of semi-discrete third-order relaxation schemes are presented for relaxation systems which approximate systems of hyperbolic conservation laws. These schemes for the scalar conservation law are shown to satisfy the property of total variation diminishing (TVD) in the zero relaxation limit. A third-order TVD Runge-Kutta splitting method is developed for the temporal discretization of the semi-discrete schemes. Numerical results are given illustrating these schemes on one-dimensional nonlinear problems.