Shock waves analysis of planar and non planar nonlinear Burgers’ equation using Scale-2 Haar wavelets
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 7 August 2017
Abstract
Purpose
This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave.
Design/methodology/approach
First, the authors discritize the time-dependent term using Crank–Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method.
Findings
Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers’ equation and yields results better than other methods and compatible with the exact solutions.
Originality/value
The numerical results for non-planar Burgers’ equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers’' equation.
Keywords
Acknowledgements
The authors express their sincere gratitude to the anonymous reviewers and editors for their valuable suggestions toward the improvement of the paper.
Citation
Pandit, S., Kumar, M., Mohapatra, R.N. and Alshomrani, A.S. (2017), "Shock waves analysis of planar and non planar nonlinear Burgers’ equation using Scale-2 Haar wavelets", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 8, pp. 1814-1850. https://doi.org/10.1108/HFF-05-2016-0188
Publisher
:Emerald Publishing Limited
Copyright © 2017, Emerald Publishing Limited