Page 66 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

Chapter 2

DYNAMICS OF INVISCID FLUIDS

The inviscid (ideal) fluids are hypothetical fluids in which the viscosity
is neglected and consequently there is no opposition while the fluid layers
slide “one on another”. Although such fluids don’t occur in nature, their

study offers useful information in the regions far enough from the solid
surfaces embedded in fluids. At the same time the neglect of viscosity
(i.e., all the coefficients of viscosity are zero) simplifies considerably the
flow equations (Euler) which allows a deep approach via the classical
calculus. Nowadays the interest has been renewed in inviscid fluid flows
because up-to-date computers are capable of solving their equations,

without any other simplifications for problems of great practical interest.
It is also interesting to note that for R’ = oo (the inviscid fluid case)
we have accomplished the conditions for a “perfect continuum”, the
Knudsen number K,, being zero [153].

The target of this chapter is to set up the main results coming from
the Euler flow equations which allows a global understanding of flow
phenomena in both the incompressible and compressible case. Obvi-
ously, due to the high complexity of the proposed aim, we will select
only the most important results within the context of numerical and
computational methods.

1. Vorticity and Circulation for Inviscid Fluids.

The Bernoulli Theorems

Suppose that in the equations of vorticity under the hypothesis that
the external forces derive from a potential, which means in