Some Finite Difference Methods for One Dimensional Burger’s Equation for Irrotational Incompressible Flow Problem

M. Rafiq, M. O. Ahmed, R. Siddique, A. Pervaiz, S. Ahmed

Abstract


In this paper special case of famous Burgers’ Equation in one dimension is solved numerically by three approaches which are FTCS explicit scheme, BTCS implicit scheme and Mac-Cormack explicit scheme. The equation in itself is important to understand the concept of fluid flow with constant pressures and irrotational flows. Four cases are discussed here. These are for four different times i.e., T = 0.1, 0.4, 0.7, 1.0. Results for these cases analyzed and shown in the form of plots. Numerical results show that the BTCS implicit method seems more accurate over the others for the cases discussed.

Full Text:

PDF

References


Pany, A. K, Neela, N & Sangita, S. A New Mixed Finite Element Method for Burgers’ Equation. J. Appl. Math. & Computing Vol. 23, No. 1 - 2, pp. 43 – 55,(2007).

Burgers, J. M. A Mathematical Model Illustrating the Theory of Turbulence. Advances in Applied Mechanics, Academic Press, New York 1, 171-199(1948).

Burgers, J. M. Mathematical Examples Illustrating Relations Occurring in the Theory of Turbulent Fluid Motion, Trans. Roy. Neth. Acad. Sci. Amsterdam 17, 1-53(1939).

Jeanne, A. A, Jeffrey T. B & Belinda, B. K. Reduced Order Controllers for Burgers’ Equation with A Nonlinear Observer. Int. J. Appl. Math. Comput. Sci., , Vol.11, No.6, 1311-1330(2001).

Anderson, D.A, Tannhill, J.C & Plecher, R.H. Computational Fluid Mechanics and Heat Transfer. Hemisphere publishing corporation McGraw Hill Book Company (1984).






Copyright (c) 2016 M. Rafiq

Powered By KICS