Contents

1 Introduction

1.1 System setting

1.1.1 OS system

1.1.2 Computational language

1.1.3 Visualization

2 Governing equations

2.1 Compact and differential form

2.2 Vector and conservative form

2.3 Equations of state

2.4 Incompressible flow

3 Numerical methods

3.1 Finite volume method vs Finite difference method

3.2 Spatial discretisation

3.2.1 Discretisation of convective fluxes

3.2.2 Discretisation of viscous fluxes

3.3 Temporal discretisation

3.3.1 Explicit time-stepping scheme

3.3.2 Implicit time-stepping scheme

4 Turbulence modelling

4.1 Basic equations of turbulence

4.2 Spalart-Allmaras model

5 Boundary conditions

5.1 Solid wall

5.2 Inlet/outlet boundary

6 Numerical tests

6.1 Cylinder

6.1.1 Inviscid vs viscous flow

6.2 Airfoil

6.2.1 Inviscid vs viscous flow