Chapter 18 - COMPUTATIONAL FLUID DYNAMICS

Abstract

The fundamental equations for incompressible flows of Newtonian fluids are the momentum and the continuity equations. These equations are written in the primitive variables of velocity components and pressure, with reference to an Eulerian frame, that is, a space-fixed system of coordinates through which the fluid flows. In primitive variable formulations, methods based on a consistent mass representation and an implicit time integration procedure have been extensively studied in the literature. The development of finite element methods (FEM) for the numerical simulation of viscous, incompressible laminar flows has received considerable attention, particularly the treatment of pressure in the primitive variable formulation. Finite element methods applied to the Navier-Stokes (NS) equations, using the velocity and pressure primitive variables can be categorized into three groups: (1) the mixed interpolation methods, (2) the penalty methods, and (3) the segregated velocity-pressure solution methods. Fully implicit finite element methods for solving transient fluid flow problems are often stable for any positive value of the time increment. However, these integrated solution techniques are not always economically feasible. Alternatively, a few explicit and semi-implicit finite element analyses based on the segregated velocity-pressure solution method have appeared. This chapter discusses different segregated approaches with emphasis on the solution implementation in the finite element context. These iterative schemes generally require much less execution time and storage than the classical velocity-pressure integrated and mixed interpolation methods, particularly for three-dimensional problems.