A Dual Wavelet Shrinkage Procedure for Suppressing Numerical Oscillation in Shock Wave Calculation

ZHAO Yong; ZONG Zhi>; WANG Tian-lin

doi:10.3879/j.issn.1000-0887.2014.06.004

Volume 35 Issue 6

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ZHAO Yong, ZONG Zhi>, WANG Tian-lin. A Dual Wavelet Shrinkage Procedure for Suppressing Numerical Oscillation in Shock Wave Calculation[J]. Applied Mathematics and Mechanics, 2014, 35(6): 620-629. doi: 10.3879/j.issn.1000-0887.2014.06.004

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A Dual Wavelet Shrinkage Procedure for Suppressing Numerical Oscillation in Shock Wave Calculation

doi: 10.3879/j.issn.1000-0887.2014.06.004

¹Transportation Equipment and Ocean Engineering College, Dalian Maritime University, Dalian, Liaoning 116026, P.R.China;²School of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China;³State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Basic Research Program of China (973 Program)(2013CB036101); The National Natural Science Foundation of China(51309040; 51379033; 51379025)

Received Date: 2014-01-21
Rev Recd Date: 2014-02-06
Publish Date: 2014-06-11

Abstract

Abstract

In the numerical calculation of shock waves, numerical oscillation often occurred and contaminated the real solution in serious cases. For the purpose of suppressing the numerical oscillation, various complicated numerical schemes or artificial viscosity methods had been applied. From the view of signal processing, a dual wavelet shrinkage procedure was formulated to extract the real solution hidden in the numerical solution with oscillation. The localized differential quadrature (LDQ) method was firstly used to solve the shock wave problems governed by the shallow water equations and Euler equations for ideal fluid flow, and heavy oscillation emerged in these cases, then the dual wavelet shrinkage procedure was employed to supplement the LDQ method and the results without numerical oscillation were obtained, in which not only the position of shock/rarefaction wave was captured but the shock wave structure well kept. Compared with the previous complicated schemes, the present procedure enables some relatively simple scheme such as the LDQ method to effectively solve the shock wave problems.
- shock wave,
- numerical oscillation,
- wavelet shrinkage method,
- localized differential quadrature,
- shallow water equation,
- Euler equation

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References(26)

References

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