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