chapter  1
54 Pages

Introduction

BySaad A. Ragab, Hassan E. Fayed

Various numerical methods have been developed to deal with certain classes of problem in each discipline of mechanics. Popular among these methods are panel methods (or boundary integral methods), finite difference, finite volume, and finite element methods. This chapter presents the basic features of these methods. The basic feature of the finite difference method is that derivatives of a function are approximated by differences of the functions at discrete points; thereby, a differential equation is replaced by an algebraic system. The finite-volume method uses integral statements of the basic laws. The domain of interest is divided into small elements. Volume averages of different variables are defined, and the integral statements are reduced to algebraic systems that may be linear or nonlinear. Mathematical formulation of the basic principles gives rise to partial differential equations in terms of kinematic variables, thermodynamic variables, and sources of momentum and energy.