TABLE OF CONTENTS In this chapter we are concerned with steady-state and transient solutions for equations of the type
where in general ? is the basic dependent, vector-valued variable, Q is a source or reaction term vector and the flux matrices F and G are such that
and in general
In the above, x i and i refer, in the indicial manner, to Cartesian coordinates and quantities associated with these. A linear relationship between the source and the scalar variable in Eq. (2.2b) is frequently referred to as a reaction term.
The general equation (2.1) can be termed the transport equation with F standing for the convective and G for the diffusive flux quantities.
Equation (2.1) is a set of conservation laws arising from a balance of the quantity ? with its fluxes F and G entering and leaving a control volume. Such equations are typical of fluid mechanics which we have discussed in Chapter 1. As such equations may also arise in other physical situations this chapter is devoted to a general discussion of their approximate solution.
The simplest form of Eqs (2.1), (2.2a) and (2.2b) is one in which the unknown is a scalar. Most of this chapter is devoted to the solution of such equations. Throughout this book we shall show that there is no need dealing with convection of vector type quantities. Thus, for simplicity we may consider the form above
