Finite Element Techniques for Fluid Flow

156 BASIC PRINCIPLES AND GOVERNING EQUATIONS

n

A

Mass flow = yoifcd S

=

/>a

ni

iidS

Fixed domain

X\

Figure 4.6

Volume

definition

The stress components consist of pressure and friction terms. We

write

(4.49)

where T

U

denotes the viscous components. Later, we shall include

additional dissipative terms due to turbulence in

τ

0

·.

The momentum

equations are now

(4.50)

with

If the τ

0

· terms are neglected, the fluid is said to be frictionless or

inviscid.

For this case,

(4.51)

and the stress transformation relations reduce to

(4.52)

According to (4.52), an inviscid fluid cannot resist a tangential

boundary surface force, i.e. one can apply only a norma ...