Shock Waves Analysis Of Planar And Non Planar Nonlinear Burgers' Equation Using Scale-2 Haar Wavelets
Keywords
Crank-Nicolson method; Gauss elimination; Nonlinear Burgers' equation; Quasilinearization technique; Scale-2 Haar wavelets
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.
Publication Date
1-1-2017
Publication Title
International Journal of Numerical Methods for Heat and Fluid Flow
Volume
27
Issue
8
Number of Pages
1814-1850
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1108/HFF-05-2016-0188
Copyright Status
Unknown
Socpus ID
85029332998 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/85029332998
STARS Citation
Pandit, Sapna; Kumar, Manoj; Mohapatra, R. N.; and Alshomrani, Ali Saleh, "Shock Waves Analysis Of Planar And Non Planar Nonlinear Burgers' Equation Using Scale-2 Haar Wavelets" (2017). Scopus Export 2015-2019. 5401.
https://stars.library.ucf.edu/scopus2015/5401