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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 6

Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Square Cavity Using Stream Function-Vorticity Formulation

Vusala Ambethkar
Manoj Kumar
Pages
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Publication Date
2017-06-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

For flows at Reynolds number $Re$=100, our numerical solutions are compared with established steady state results and excellent agreement is obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a streamfunction-vorticity $(\psi-\xi)$ method is suitably used to investigate the problem of 2-D steady viscous incompressible flow in a driven square cavity with moving top and bottom wall.
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Key Findings & Data:A general algorithm was used for this method in order to compute the numerical solutions for streamfunction $\psi$, vorticityfunction $\xi$ for low Reynolds numbers $Re \leq 100$.
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Conclusion & Impact:For flows at Reynolds number $Re$=100, our numerical solutions are compared with established steady state results and excellent agreement is obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Stream function-vorticity formulation · numerical solutions · geometric center of square cavity

Abstract

In this study, a streamfunction-vorticity $(\psi-\xi)$ method is suitably used to investigate the problem of 2-D steady viscous incompressible flow in a driven square cavity with moving top and bottom wall. We used this method to solve the governing equations along with no-slip and slip wall boundary conditions at low Reynolds number. A general algorithm was used for this method in order to compute the numerical solutions for streamfunction $\psi$, vorticityfunction $\xi$ for low Reynolds numbers $Re \leq 100$. We have executed this with the aid of a computer programme developed and run in C++ compiler. We have also proposed the stability criterion of the numerical scheme used. Streamline, vorticity and isobar contours have been depicted at different low Reynolds numbers. For flows at Reynolds number $Re$=100, our numerical solutions are compared with established steady state results and excellent agreement is obtained.

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Cite This Article

Ambethkar, V., Kumar, M. (2017). Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Square Cavity Using Stream Function-Vorticity Formulation. Turkish Journal of Mathematics and Computer Science, Volume: 6. https://ajindex.com/articles/1324968

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