Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis
Joint Authors
Su, Shaojuan
Wang, Tianlin
Zhao, Yong
Yu, Peng-Yao
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-02
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
In the numerical solution for nonlinear hyperbolic equations, numerical oscillation often shows and hides the real solution with the progress of computation.
Using wavelet analysis, a dual wavelet shrinkage procedure is proposed, which allows one to extract the real solution hidden in the numerical solution with oscillation.
The dual wavelet shrinkage procedure is introduced after applying the local differential quadrature method, which is a straightforward technique to calculate the spatial derivatives.
Results free from numerical oscillation can be obtained, which can not only capture the position of shock and rarefaction waves, but also keep the sharp gradient structure within the shock wave.
Three model problems—a one-dimensional dam-break flow governed by shallow water equations, and the propagation of a one-dimensional and a two-dimensional shock wave controlled by the Euler equations—are used to confirm the validity of the proposed procedure.
American Psychological Association (APA)
Zhao, Yong& Yu, Peng-Yao& Su, Shaojuan& Wang, Tianlin. 2018. Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1207712
Modern Language Association (MLA)
Zhao, Yong…[et al.]. Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis. Mathematical Problems in Engineering No. 2018 (2018), pp.1-8.
https://search.emarefa.net/detail/BIM-1207712
American Medical Association (AMA)
Zhao, Yong& Yu, Peng-Yao& Su, Shaojuan& Wang, Tianlin. Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1207712
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1207712