The Discretization Process

Abstract

This chapter introduces the different steps of the discretization process, which include: (i) modeling of the geometric domain and the physical phenomena of interest; (ii) discretization of the modeled geometric domain into a grid or mesh that forms the computational domain (this process, also known as meshing or domain discretization, results in a set of non-overlapping elements, denoted also by cells, that cover the computational domain); (iii) numerical or equation discretization that transforms the set of conservation partial differential equations governing the physical processes into an equivalent system of algebraic equations defined over each of the elements of the computational domain; and (iv) the solution of the resulting set of equations using an iterative solver to yield an intermediate or final solution field. Throughout the chapter, computer implementation issues are introduced.