ABSTRACT
The Þeld of ßuid mechanics is concerned with the motion of ßuids and their effect on the surroundings. A ßuid state of matter is often characterized by the relative mobility of the molecules that constitute the matter. Fluids exist either in the form of a gas or a liquid; more complex materials, such as mixtures, may also have a ßuid behavior. In this chapter, Þnite element models are developed based on the weak formulation of the equations of viscous, incompressible ßuids under isothermal conditions. The motion of a ßuid is governed by the global laws of conservation of mass,
momenta, and energy (see Chapter 1). These equations consist of a set of coupled, nonlinear, partial differential equations in terms of the velocity components, temperature, and pressure. When temperature effects are not important, the energy equation is uncoupled from the momentum (i.e., the Navier—Stokes) equations. Thus for isothermal ßows, we need to solve only the Navier—Stokes equations and continuity equation. When the Reynolds number for the ßow is very low, the nonlinear terms due to inertial effects can be neglected, resulting in a linear boundary value problem. Such a ßow is termed Stokes ßow.
