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Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization

Published online by Cambridge University Press:  28 May 2015

Changna Lu  and
Gang Li
Changna Lu*
Affiliation:
College of Mathematics & Physics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044, P.R. China
Gang Li*
Affiliation:
School of Mathematical Science, Qingdao University, Qingdao 266071, P. R. China
*
Corresponding author.Email address:luchangna@nuist.edu.cn
Corresponding author.Email address:gangli1978@163.com
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Abstract

In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory (WENO) schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms. Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values. Extensive simulations are performed, which indicate that, the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy, and are more cost effective than WENO scheme with Runge-Kutta time discretization, while still maintaining nonoscillatory properties.

Keywords

65M1078A48Multilevel time discretizationweighted essentially non-oscillatory schemesshallow water equationsRunge-Kutta methodhigh order accuracy
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011 , pp. 505 - 524
Copyright
Copyright © Global Science Press Limited 2011

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