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

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. Moreo...

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Bibliographic Details
Published in:IEEE access 2017, Vol.5, p.7139-7148
Main Authors: Saqib, Muhammad, Hasnain, Shahid, Mashat, Daoud Suleiman
Format: Article
Language:English
Subjects:
ADI method
Alternating direction implicit methods
Convection
Convection-diffusion equation
Convergence
Crank-Nicholson method
Difference equations
Diffusion
finite difference method
Implicit methods
Iterative methods
Mathematical analysis
Mathematical model
Newton’s method
Nonlinear equations
Nonlinear systems
Numerical stability
Stability analysis
Time dependence
Two dimensional displays
Unsteady convection-diffusion equations
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Summary: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.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2017.2699320