Finite Volume Method (FVM) in CFD

1. Introduction to FVM

• Fundamental numerical method in CFD
• Step-by-step approach through practical examples
• Focus on discretization techniques and solution methods

2. Example 1: Heat Transfer in a Solid Rod A. Problem Setup

• 1D rod with fixed temperatures (20°C and 100°C)
• Length: 6 cm
• Steady-state heat conduction

B. Solution Methodology

• Transport equation simplification
• Pure diffusion case
• Domain discretization into 6 control volumes
• Node identification system (W, P, E notation)

C. Discretization Process

• Interface calculations
• Cell central differencing
• Temperature gradient calculations
• Boundary condition handling

3. Key FVM Concepts Demonstrated A. Grid Generation

• Control volume division
• Node placement
• Face positioning

B. Discretization Techniques

• Taylor series expansion
• Central differencing scheme
• Interface property calculations

C. Numerical Implementation

• Matrix formulation
• Boundary condition treatment
• Solution verification

4. Advanced Applications A. Cooling Fin Analysis

• Convective heat transfer
• Variable boundary conditions
• Heat transfer coefficient effects

B. Channel Flow Analysis

• Momentum equations
• Velocity boundary conditions
• Flow field calculations

5. FVM Advantages

• Conservation principles inherently satisfied
• Complex geometry handling
• Straightforward physical interpretation
• Direct relationship to transport phenomena

6. Practical Considerations

• Grid quality importance
• Boundary condition implementation
• Solution accuracy and convergence
• Numerical stability

7. Implementation in Commercial Software

• Connection to ANSYS Fluent methods
• Industry-standard practices
• Practical applications

This structured approach demonstrates FVM’s application from basic heat transfer to complex fluid flow problems, providing a foundation for understanding commercial CFD software implementations.