Solving shallow water equations with crisp and uncertain initial conditions
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 8 October 2018
Issue publication date: 30 October 2018
Abstract
Purpose
This paper aims to deal with the application of variational iteration method and homotopy perturbation method (HPM) for solving one dimensional shallow water equations with crisp and fuzzy uncertain initial conditions.
Design/methodology/approach
Firstly, the study solved shallow water equations using variational iteration method and HPM with constant basin depth and crisp initial conditions. Further, the study considered uncertain initial conditions in terms of fuzzy numbers, which leads the governing equations to fuzzy shallow water equations. Then using cut and parametric concepts the study converts fuzzy shallow water equations to crisp form. Then, HPM has been used to solve the fuzzy shallow water equations.
Findings
Results obtained by both methods HPM and variational iteration method are compared graphically in crisp case. Solution of fuzzy shallow water equations by HPM are presented in the form triangular fuzzy number plots.
Originality/value
Shallow water equations with crisp and fuzzy initial conditions have been solved.
Keywords
Citation
Karunakar, P. and Chakraverty, S. (2018), "Solving shallow water equations with crisp and uncertain initial conditions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 12, pp. 2801-2815. https://doi.org/10.1108/HFF-09-2017-0351
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited