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

Authors

Maan A. Rasheed, Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, IraqFollow
Suad Naji Kadhim, Department of Mathematics, College of Science, University of Baghdad, Baghdad, IraqFollow

Abstract

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.

Keywords

Finite difference, Reynolds number, Stream function, Truncation error, Vorticity function.

Article Type

Article

How to Cite this Article

Rasheed, Maan A. and Kadhim, Suad Naji (2022) "Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method," Baghdad Science Journal: Vol. 19: Iss. 2, Article 23.
DOI: https://doi.org/10.21123/bsj.2022.19.2.0321