Numerical Study On Polar Driven Cavity Flow
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Date
2025
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Department of Mathematics, NITS
Abstract
In this paper, we present the mathematical formulation and numerical approach for solving the two-dimensional steady incompressible Navier–Stokes equations in stream function–vorticity form for flow inside a polar cavity bounded by concentric circular walls. The study focuses on the annular region between the inner and outer walls, where the flow is driven by motion along the boundaries. The governing equations, expressed in cylindrical coordinates, are discretized using a finite difference scheme on a fine uniform grid. Particular attention is given to the treat ment of boundary conditions and the iterative solution strategy to ensure numerical stability and accuracy at high Reynolds numbers.” In chapters 1 and 2, we discuss about the basic terminology introduction, literature survey. In chapter 3 we discuss the mathematical formulation and boundary condition. In Chapter 4 we presents a finite difference approach for solving 2D steady incompressible flow in a polar cavity using the stream function–vorticity formulation. The stream function is modeled as a Poisson equation, while vorticity is treated as a convection–diffusion equation. Numerical schemes ensure stability and accuracy across different Reynolds numbers. Chapter 5 presents the results and discussion, including numerical validation and comparison between numerical and experimental solutions. Vorticity plots are analyzed for various Reynolds numbers, along with stream function and vorticity contours to visualize flow behavior in the polar cavity.