Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method

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Maan A. Rasheed
Suad Naji Kadhim


This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.


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Rasheed MA, Kadhim SN. Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method. Baghdad Sci.J [Internet]. 2022 Apr. 1 [cited 2023 Oct. 4];19(2):0321. Available from:


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