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http://dx.doi.org/10.4134/BKMS.2008.45.4.781

ADAPTIVE MESH REFINEMENT FOR WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEMES  

Yoon, Dae-Ki (DEPARTMENT OF MATHEMATICS KOREA UNIVERSITY)
Kim, Hong-Joong (DEPARTMENT OF MATHEMATICS KOREA UNIVERSITY)
Hwang, Woon-Jae (DEPARTMENT OF INFORMATION AND MATHEMATICS KOREA UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 781-795 More about this Journal
Abstract
In this paper, we describe the application procedure of the adaptive mesh refinement (AMR) for the weighted essentially non-oscillatory schemes (WENO), and observe the effects of the derived algorithm when problems have piecewise smooth solutions containing discontinuities. We find numerically that the dissipation of the WENO scheme can be lessened by the implementation of AMR while the accuracy is maintained. We deduce from the experiments that the AMR-implemented WENO scheme captures shocks more efficiently than the WENO method using uniform grids.
Keywords
WENO scheme; adaptive mesh refinement; conservation laws;
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