ABSTRACT
This chapter presents an overview of the coordinate transformation relations appropriate for the transformation of partial differential equations encountered in heat transfer applications. It also presents the numerical grid-generation technique, and illustrates the basic concepts in grid generation and mapping, by considering a one-dimensional simple transformation utilizing algebraic relations. However, it is difficult to develop analytic transformations capable of clustering grids around arbitrary locations, whereas the numerical grid-generation technique provides a unified approach for developing transformations capable of dealing with more general situations. The chapter also illustrates the application of the numerical grid-generation technique to transform the irregular physical region into a regular one in the computational domain and solve the free convection problem with finite differences over the regular region. Therefore, positions of the control volume center and the control volume surface center are evaluated in the transformed domain during the grid-generation procedure, thus avoiding the use of coordinate averaging within the physical domain.
