Numerical generation of orthogonal boundary-fitted grids for heat and fluid flow

We report on the efficiency and flexibility of a grid generation method for two-dimensional or axisymmetric domains of arbitrary shape. Based on an algorithm first proposed by G. Ryskin and L.G. Leal (1983) and on a standard implicit finite-difference numerical scheme (ADI), we set up a robust and efficient numerical code to generate orthogonal computational grids that conform to the boundaries of the physical domain. Several applications of computational fluid mechanics and heat transfer in simply- and doubly-connected geometries serve to suggest that the method can compete with finite-element methods in terms of efficiency, clarity and economy. This paper further demonstrates that our numerical scheme can be used for the solution of realistic problems in computational physics on desktop computers. The numerical package is open-ended and has a user-friendly interface with a variety of interactive graphical tools.