# 4.1.1. CFD¶

## 4.1.1.1. What is Fluid Mechanics?¶

A science and branch of physics concerning:

• Fluids - liquids or gases

• Mechanics - application of laws of force and motion

There are two branches of fluid mechanics:

• Fluid statics - fluids at rest

• Fluid dynamics - fluids in motion

## 4.1.1.2. What is Thermodynamics?¶

A science and branch of physics concerning:

• Heat

• Work

And their relation to variables such as:

• Internal energy

• Enthalpy

• Entropy

## 4.1.1.3. What is CFD?¶

A science and branch of fluid mechanics and thermodynamics to predict fluid flow using:

• Conservation laws

• Numerical methods

• Algorithms

• Digital computers

## 4.1.1.4. What are the reasons for using CFD?¶

Allows virtual experiments that in the real world would be:

• Difficult

• Dangerous

• Expensive

• Impossible

## 4.1.1.5. What are the steps in a CFD process?¶

• Physical model - describe physical model

• Mathematical model - describe equations that correspond with physical model

• Numerical methods - describe numerical methods that correspond with physical model and implement in code

• Geometry/Grid - describe grid that corresponds with physical model and implement in code

• Numerical solver - describe solver that corresponds with physical model and implement in code and compute solution

• Verification - establish solution validity

• Validation - compare with experimental data

## 4.1.1.6. Why do vector calculus and linear algebra play important roles in CFD?¶

Vector calculus is important in CFD because it allows description e.g.

• Vector field - velocity of a flow

• Divergence of a flow field - expansion or compression of a flow

• Curl of a flow field - rotation of a flow

Linear algebra is important in CFD because it allows solution of the description of the flow e.g.

• Eigenvalues - charactersitic speeds of a system of hyperbolic equations

• Eigenvectors - characteristic directions of a system of hyperbolic equations

• TDMA - solution of tri-diagonal systems (e.g. Navier-Stokes momentum equation)

## 4.1.1.7. What can go wrong in CFD?¶

• Over-simplicifcation - Simplify domain to look only at part of system not the whole system

• Numerical error - Numerics introduces dissipation or dispersion

• Geometry/grid - Errors due to coordinate transformation