ABSTRACT
This chapter focuses on the formulation of the numerical method for general two-dimensional situations; it will be useful to study the solution of one-dimensional heat conduction. When only a small number of grid points are used to discretize the calculation domain, the discretization equations represent an approximation to the differential equation. The strength of a numerical method lies in the replacement of the differential equation by a set of algebraic equations, which are easier to solve. When the discretization equations are derived by the control-volume method, they represent the conservation of energy, momentum, mass, etc. for each control volume. It then follows that the resulting numerical solution correctly satisfies the conservation of these quantities over the whole calculation domain. A numerical solution obtained with only a small number of grid points will exhibit some error with reference to the exact solution. The chapter discusses a number of advanced features in the one-dimensional context.
