Title: Comparison of the LBM with the modified local Crank-Nicolson method solution of transient one-dimensional nonlinear Burgers' equation

Authors: Ahmad Reza Haghighi; Shirin Pakrou

Addresses: Department of Mathematics, Urmia University of technology, P.O. Box, 57155-419, Urmia, Iran ' Department of Mathematics, Urmia University of technology, P.O. Box, 57155-419, Urmia, Iran

Abstract: Burgers' equation is a simplified form of the Navier-Stokes equations that represents the nonlinear features of them. In this paper, the transient one-dimensional nonlinear Burgers' equation is solved using the lattice Boltzmann method (LBM). The results are compared with the modified local Crank-Nicolson method (MLCN) and exact solutions. An example, distinguished by initial condition, is solved using the LBM and the MLCN methods and the accuracy of these two methods at various Reynolds numbers are analysed. Also, the effects of different numbers of particle velocities on the accuracy of the LBM are evaluated. The results show that at higher Reynolds numbers the accuracy of the LBM is higher than the MLCN method and vice versa.

Keywords: Burgers equation; MLCN method; LBM; lattice Boltzmann method; explicit method; unconditionally stable; modified local Crank-Nicolson; Reynolds numbers; particle velocities.

DOI: 10.1504/IJCSM.2016.080084

International Journal of Computing Science and Mathematics, 2016 Vol.7 No.5, pp.459 - 466

Received: 29 Dec 2014
Accepted: 10 Nov 2015
Published online: 01 Nov 2016 *

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