Numerical Analysis of Cavity Flow: A CFD Case Study

1. Problem Description and Setup

A. Geometric Configuration

• Rectangular cavity dimensions
• Mesh characteristics
• Domain specifications

B. Boundary Conditions

• Top wall: Specified velocity
• Side and bottom walls: No-slip
• Fluid properties:
  • Density: 1000 kg/m³
  • Viscosity: 0.001 Pa·s

2. Numerical Methodology

A. Solution Framework

• SIMPLE algorithm implementation
• Second-order central differencing
• 2D Navier-Stokes equations

B. Implementation Strategy

• Momentum equations (x and y)
• Pressure correction equation
• Variable initialization process

3. Solution Process

A. Algorithmic Components

• Iterative procedure
• Convergence criteria
• Under-relaxation factors

B. Stability Considerations

• Convergence rate optimization
• Numerical stability
• Parameter adjustment

4. Analysis and Results

A. Flow Visualization

• Velocity vector distribution
• U-velocity contour plots
• Convergence monitoring

B. Case Variations

• Standard cavity configuration
• Dimensional modifications
• Alternative boundary conditions:
  • Symmetric velocities
  • Opposing flow patterns

5. Engineering Applications

A. Physical Phenomena

• Vortex formation mechanics
• Flow pattern development
• Geometric influence

B. Practical Implications

• Engineering design applications
• Performance optimization
• Design guidelines

This comprehensive analysis provides valuable insights into cavity flow behavior and demonstrates practical CFD application for engineering problems.