ABSTRACT
This chapter focuses on finite difference formulation, solution, and stability considerations of one-dimensional transient systems. The transient problems have numerous important applications in various branches of science and engineering. The chapter discusses problems dealing with pure diffusion, pure advection, and advection plus diffusion, with parabolic and hyperbolic behaviors. It addresses cases where fluid flow influences the transport of the conserved quantity in transient one-dimensional problems. Although the Taylor series and the finite control volume approaches for the discretization of the governing equations are applicable to the cases examined, care must be exercised with respect to the discretization of advective terms, which actually gave rise to several discretization schemes in the past. The chapter examines both the purely advective equation and the advective–diffusive equations. It applies the finite volume method described to discretize the advective–diffusive equation.
