Highly Efficient Computational Methods for Two Dimensional Coupled Nonlinear Unsteady Convection-Diffusion Problems

Abstract

In this paper, a numerical solution of 2-D time-dependent coupled nonlinear system is discussed. Both Crank-Nicholson and alternating direction implicit methods were used to address the problems associated with nonlinear system. These schemes depict the second-order accuracy in space and time. Moreover, system of these equations that is concerned with the implicit scheme is very efficient and reliable for solving 2-D nonlinear coupled convection diffusion equations. In this system, algebraic difference equations are solved at each time level. In fact, in this paper, these methodologies were unified with iterative methods to resolve nonlinear systems. The procedures have been analyzed for their stability and convergence. Numerical results showed that the proposed alternating direction implicit scheme was very efficient and reliable for solving 2-D nonlinear coupled convection diffusion equations. The proposed methods can be implemented for fixing nonlinear problems arising in engineering and physics.

Keywords

• Unsteady convection-diffusion equations
• Crank-Nicholson method
• ADI method
• finite difference method
• Newton’s method