An introduction to computational fluid mechanics

1. Introduction

2. Governing Equations

2.1. Fluid Flow Equations
2.2. Differential and Integral Form of the General Transport Equation
2.3. Classification of Physical Behaviour
2.4. Classification of Fluid Flow Equations
2.5. Boundary Conditions for Viscous Flow

3. Finite Volume Method for Convection-Diffusion Problems

3.1. FVM for 1-D steady diffusion
3.2. FVM for 2-D diffusion problems
3.3. FVM for 3-D diffusion problems

4. Finite Volume Method for Convection-Diffusion Problems

4.1. Steady 1-D Convection and Diffusion
4.2. The Central Differencing Scheme
4.3. Properties of Discretisation Scheme
4.4. Assesment of Central Differencing Scheme for Convection-Diffusion Problems
4.5. The Upwind Differencing Scheme
4.6. The Hybrid Differencing Scheme
4.7. Hybrid Differencing Scheme for Multi- Dimensional Convection Diffusion
4.8. The power-Law Sheme
4.9. Other Schemes of Higher Order

5. Pressure-Velocity Coupling in Steady Flows

5.1. The Staggered Grid
5.2. The Momentum Equations
5.3. The SIMPLE algorithm
5.4. The SIMPLER algorithm
5.5. Comments and Remarks
5.6. The case of Co-located Grid

6. Solution of Discretised Equations

6.1. The Tri-Diagonal Matrix Algorithm
6.2. Application of TDMA to 2-D problems
6.3. Application of TDMS to 3-D problems
6.4. The Converge Criterion

7. The Finite Volume Method for Unsteady Flows

7.1. One-Dimensional Unsteady Heat Conduction
7.2. Implicit Method for 2-D and 3-D problems
7.3. Discretisation of Transient Convection-Diffusion Equation
7.4. Transient SIMPLE

8. Implementation of Boundary Conditions

8.1. Inlet Boundary Conditions
8.2. Outlet Boundary Conditions
8.3. Wall Boundary Conditions
8.4. The Constant Pressure Boundary Condition
8.5. Symmetry and Periodic Boundary Conditions
8.6. Final Remarks

9. A Brief CFD Gallery

Bibliography