TABLE OF CONTENTS Having defined in Part I, the mathematical models for fluid dynamics and a methodology for analyzing their fundamental properties in Chapter 3, we are now ready to move on to the next step toward setting up a CFD algorithm, namely the discretization phase.
As outlined in Figures I.2.1 and I.3.1, to which we refer you again, this second step in the definition of the computational approach deals with the choice of the discretization method of the selected mathematical model and involves two components, the space discretization and the equation discretization.
The space discretization consists in setting up a mesh, or a grid, by which the continuum of space is replaced by a finite number of points where the numerical values of the variables will have to be determined. It is intuitively obvious that the accuracy of a numerical approximation will be directly dependent on the size of the mesh, that is the closer the points, the better the discretized space approaches the continuum, the better the approximation of the numerical scheme. In other words, the error of a numerical simulation has to tend to zero when the mesh size tends to zero, and the pace of this variation will be characterized by the order of the numerical discretization.
For complex...
