Fortran Subroutine for the Solution of Periodic Block-Tridiagonal Systems

The numerical simulation of the flow past an arbitrary airfoil (if a numerical grid generation technique is employed) or a turbomachinery cascade, by means of block-Alternating Direction Implicit (ADI) methods, requires the numerical solution of large numbers of cyclic block-tridiagonal systems. A method for the extension of the so-called Thomas algorithm to a cyclic tridiagonal system is given by H. H. Ahlberg et al. The present work provides the implementation of the approach of Ahlberg et al. generalized to the case of a block-tridiagonal system of arbitrary block size. The algorithm is briefly outlined and a Fortran subroutine implementing it is provided. A model problem is employed to verify the correctness of the enclosed Fortran subroutine.