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Journal of Applied Mathematics
Volume 2014, Article ID 275425, 13 pages
http://dx.doi.org/10.1155/2014/275425
Research Article

Simple and High-Accurate Schemes for Hyperbolic Conservation Laws

LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Received 1 May 2013; Revised 4 January 2014; Accepted 6 January 2014; Published 2 March 2014

Academic Editor: Vit Dolejsi

Copyright © 2014 Renzhong Feng and Zheng Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper constructs a class of simple high-accurate schemes (SHA schemes) with third order approximation accuracy in both space and time to solve linear hyperbolic equations, using linear data reconstruction and Lax-Wendroff scheme. The schemes can be made even fourth order accurate with special choice of parameter. In order to avoid spurious oscillations in the vicinity of strong gradients, we make the SHA schemes total variation diminishing ones (TVD schemes for short) by setting flux limiter in their numerical fluxes and then extend these schemes to solve nonlinear Burgers’ equation and Euler equations. The numerical examples show that these schemes give high order of accuracy and high resolution results. The advantages of these schemes are their simplicity and high order of accuracy.