Adaptive mesh refinement for weighted essentially non-oscillatory schemes

Daeki Yoon; Hongjoong Kim; Woonjae Hwang

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2008; 45(4): 781-795

Printed December 1, 2008

Adaptive mesh refinement for weighted essentially non-oscillatory schemes

Daeki Yoon, Hongjoong Kim, and Woonjae Hwang

Korea University

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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

MSC numbers: Primary 65M06, 65M50, 35L65