TRANSFORMATIONS FOR INFINITE REGIONS AND THEIR APPLICATION TO FLOW PROBLEMS

Three transformations are presented which map one or both of the intervals [0, ∞] and [-∞, ∞] into finite intervals. These transformations are particularly useful for the finitedifference solution of systems of differential equations involving infinite regions, since they permit straightforward application of boundary conditions at infinity, while concentrating the grid points in the region where the solution is desired. Two transformations are presented which are appropriate for the interval [0, ∞]. The third transformation may be employed for both intervals and is thus applicable to a wider variety of problems. Application of this third transformation to an implicit finite-difference solution of the laminar boundary-layer equations demonstrates the advantages of this transformation over the familiar Crocco transformation. Applications of another of the three transformations to a free-molecular-flow problem and to the incompressible Navier-Stokes equations in two dimensions are cited which illustrate the diverse problems that may be treated. © 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.