Numerical Methods and Its Solution - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 225

Fig. 7.35 Nanoparticle
deposition pattern in the
nasal-sinus cavity for 10 nm -
resulting in 29.8 %
deposition. Particles are
coloured by trajectory time
within the nasal cavity before
impacting onto the surfaces at
10 L/min

Other Plots Streamlines are used for examining the nature of a flow either in two or
three dimensions (e.g. (Fig. 7.34 b). By definition, streamlines are parallel to the mean
velocity vector where they trace the flow pattern using massless particles. They can
generally be obtained by integrating the spatial three velocity components expressed
in a three-dimensional Cartesian frame: dx/dt

= u , dy/dt = v and dz/dt = w .

Streamlines are also called streamtraces , streaklines or path lines .

Animations CFD data lends itself very neatly to the animation category - moving
pictures of the data produced through the CFD simulation. Animation, as with other
graphical display tool, represents not only a technical record of quantitative results;
it is an artistic work of art. Nowadays, a collection of short-length animated videos or
movies with multiple frames of brightly colourful representations of CFD simulations
can be found in many internet websites. It is undoubtedly an effective visualization
tool for education and marketing purposes.

7.7 Summary

In this chapter we have introduced the basic computational techniques to solve the
governing equations of fluid dynamics. The first stage of obtaining the computational
solution involves the conversion of the governing equations into a system of algebraic
equations. This is usually known as the discretisation stage . We have discussed some
of the discretisation tools such as the finite difference and finite volume methods,
which form the foundation of understanding the basic features of discretisation . Both
of these methods are abound in many CFD applications.
The second stage involves numerically solving the system of algebraic equations,
which can be achieved by either the direct methods or iterative methods . Basic direct
methods such as the Gaussian elimination and the Thomas algorithm have been
described of which the latter is highly economical for a tri-diagonal matrix system
and is a standard algorithm for the solution of fluid flow equations in a structured