CrankNicolson scheme for numerical solutions of twodimensional coupled Burgers’ equations

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Author(s) 
Vineet Kumar Srivastava, Mohammad Tamsir, Utkarsh Bhardwaj, YVSS Sanyasiraju 

KEYWORDS 
Burgers’ equations; CrankNicolson scheme; finite difference; Newton’s method; Reynolds number


ABSTRACT 
The twodimensional Burgers’ equation is a mathematical model to describe various kinds of phenomena such as turbulence and viscous fluid. In this paper, CrankNicolson finitedifference method is used to handle such problem. The proposed scheme forms a system of nonlinear algebraic difference equations to be solved at each time step. To linearize the nonlinear system of equations, Newton’s method is used. The obtained linear system is then solved by Gauss elimination with partial pivoting. The proposed scheme is unconditionally stable and second order accurate in both space and time. Numerical results are compared with those of exact solutions and other available results for different values of Reynolds number. The proposed method can be easily implemented for solving nonlinear problems evolving in several branches of engineering and science.


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