# 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