Finite Element Techniques for Fluid Flow

4 Basic Principles

and Governing

Equations of

Fluid Mechanics

4.1 EULERIAN AND LAGRANGIAN FORMULATIONS:

MATERIAL DERIVATIVE

One can specify the position of a material point with respect to a

'fixed' orthogonal reference frame as shown in Figure

4.1.

The initial

coordinates at t = 0 are a, and the coordinates at time t are x,.*

Quantities of interest such as pressure, velocity and temperature are

functions of position and time. Since there are two choices as to

position variables, the governing equations can have two different

forms.

In the Lagrange approach, the independent variables are time t

and the initial coordinates a

t

. The spatial coordinate ...