Finite Element Techniques for Fluid Flow

166 BASIC PRINCIPLES AND GOVERNING EQUATIONS

Example

4.3

We can incorporate incompressibility by weighting the continuity

equation with respect to δρ and integrating over the volume (see

Lagrangian multipliers, Chapter 1),

e

v

= 0

V (a)

^ δρ dV = 0 for arbitrary δρ

Combining (a) and (4.85) leads to

(b)

for arbitrary f, Sv

k

, δρ.

Additional variational statements are generated later on in the

chapters on finite element applications.

4.8 TURBULENCE

At this stage we will divide the flow into two general categories,

laminar

and turbulent

flow.

If the flow particles follow streamlines

which do not intersect each other, the flow is laminar. Viscou