Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics

In this chapter, we will focus on solving the PDEs governing laminar flows of viscous incompressible fluids using the FVM (this chapter is a counterpart of Chapter 6 on FEM, where velocity–pressure and penalty finite element models of two dimensional flows of viscous incompressible fluids were presented). These equations are expressed in terms of the primitive variable, namely, the velocity field and the pressure. To begin with, we will consider isothermal flows (flows without the presence of the temperature effect), and demonstrate the use of the FVM for two-dimensional laminar flows of viscous incompressible fluids. Then cases of non-isothermal flows with both forced convection and natural convection will be considered in the sequel.