Computational Fluid Dynamics Fundamentals Course

The course starts off with an introduction to the Navier-Stokes equations, which are derived from Newton's second law. The general form of transport equations for temperature, species concentration and passive scalars are then introduced. It is shown that all transport equations in CFD share a common form and can all be analysed with the same framework used in this course.

The finite volume discretisation of the 1D diffusion equation is introduced in this Lecture, for both interior and boundary cells. The finite volume equations are then assembled in matrix form (AX=B) and solved.

The finite volume discretisation of the diffusion equation from the precious lecture is extended to include the convection term. The relative strength of the convective and diffusive transport mechanisms are compared using the Peclet number. High and low Peclet number solutions are generated with central differencing and it is shown that central differencing leads to non-physical oscillations at high Peclet number.

Upwind differencing for the convection term is introduced in this Lecture and is compared with central differencing from the previous Lecture. It is shown that upwind differencing eliminates the non-physical oscillations that are generated by central differencing. However, it also leads to a reduction in accuracy as the scheme is only first order accurate.