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Journal of Computational Engineering - Volume 2015 2015, Article ID 575380, 10 pages -

Research Article

Nuclear Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan

Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign. 216 Talbot Laboratory, 104 S. Wright Street, Urbana, IL 61801, USA

Received 15 March 2015; Revised 7 June 2015; Accepted 21 June 2015

Academic Editor: Jim B. W. Kok

Copyright © 2015 Rabie A. Abu Saleem and Tomasz Kozlowski. 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.


A high-resolution, total variation diminishing TVD stable scheme is derived for scalar hyperbolic problems using the method of flux limiters. The scheme was constructed by combining the 1st-order upwind scheme and the 3rd-order quadratic upstream interpolation scheme QUICK using new flux limiter function. The new flux limiter function was established by imposing several conditions to ensure the TVD properties of the scheme. For temporal discretization, the theta method was used, and values for the parameter θ were chosen such that the scheme is unconditionally stable. Numerical results are presented for one-dimensional pure advection problems with smooth and discontinuous initial conditions and are compared to those of other known numerical schemes. The results show that the proposed numerical method is stable and of higher order than other common schemes.

Autor: Rabie A. Abu Saleem and Tomasz Kozlowski



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