Title: Comparative numerical investigation of Burgers' equation with and without Hopf-Cole transformation
Authors: Mayur P. Bonkile; Ashish Awasthi; S. Jayaraj
Addresses: Department of Mechanical Engineering, National Institute of Technology Calicut, Kozhikode pin: 673 601, Kerala, India ' Department of Mathematics, National Institute of Technology Calicut, Kozhikode pin: 673 601, Kerala, India ' Department of Mechanical Engineering, National Institute of Technology Calicut, Kozhikode pin: 673 601, Kerala, India
Abstract: Even if the numerical simulation of the unsteady viscous Burgers' equation is well documented in the literature, a detailed literature survey indicates that there is still gaps exists for comparative investigation regarding the effect of Hopf-Cole transformation on the efficiency and accuracy of schemes. In this paper, a comparative numerical investigation of Burgers' equation is presented based on two different approaches. Hopf-Cole transformation is implemented on this equation and then solved by modified Keller box scheme. We sketch a new implicit scheme with second order accuracy in space and time, which is proposed to solve Burgers' equation without using Hopf-Cole transformation. Numerical results of two test problems, which are calculated for various values of kinematic viscosity and time steps, are found to be matching with the exact solution. The new implicit box scheme is proved to be more accurate than the modified Keller box scheme with Hopf-Cole transformation based on L2 and L∞ errors.
Keywords: finite difference method; Burgers' equation; Hopf-Cole transformation; Keller box scheme; implicit box scheme; kinematic viscosity; time steps; partial differential equations; PDE.
International Journal of Convergence Computing, 2016 Vol.2 No.1, pp.54 - 78
Received: 21 May 2015
Accepted: 16 Jun 2016
Published online: 17 Nov 2016 *