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

Socpus ID

85029332998 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85029332998

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