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Shock wave simulations using Sinc Differential Quadrature Method

Alper Korkmaz (Department of Mathematics, Faculty of Science, Çankiri Karatekin University, Çankiri, Turkey)
İdris Dağ (Department of Mathematics and Computer Sciences, Eskişehir Osmangazi University, Eskişehir, Turkey)

Engineering Computations

ISSN: 0264-4401

Article publication date: 23 August 2011

Abstract

Purpose

This paper aims to present a numerical solution of non‐linear Burger's equation using differential quadrature method based on sinc functions.

Design/methodology/approach

Sinc Differential Quadrature Method is used for space discretization and four stage Runge‐Kutta algorithm is used for time discretization. A rate of convergency analysis is also performed for shock‐like solution. Numerical stability analysis is performed.

Findings

Sinc Differential Quadrature Method generates more accurate solutions of Burgers' equation when compared with the other methods.

Originality/value

This combination, Sinc Differential Quadrature and Runge‐Kutta of order four, has not been used to obtain numerical solutions of Burgers' equation.

Keywords

Citation

Korkmaz, A. and Dağ, İ. (2011), "Shock wave simulations using Sinc Differential Quadrature Method", Engineering Computations, Vol. 28 No. 6, pp. 654-674. https://doi.org/10.1108/02644401111154619

Publisher

:

Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited