Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis

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...

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Bibliographic Details
Published in:Mathematical problems in engineering 2018-01, Vol.2018 (2018), p.1-8
Main Authors: Wang, Tianlin, Su, Shaojuan, Yu, Peng-Yao, Zhao, Yong
Format: Article
Language:English
Subjects:
Applied mathematics
Computational physics
Decomposition
Engineering
Euler-Lagrange equation
Fluid dynamics
Methods
Neighborhoods
Numerical analysis
Partial differential equations
Quadratures
Rarefaction
Shallow water equations
Shock wave propagation
Shock waves
Shrinkage
Simulation
Turbulence models
Wavelet analysis
Wavelet transforms
Citations: Items that this one cites
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2018/4859469