Shock wave simulations using Sinc Differential Quadrature Method

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.

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