On the use of Cray's scientific libraries for a Navier-Stokes algorithm for complex three-dimensional geometries

In this paper some of the problems associated with the use of the linear solvers available in Gray's Scientific Library in the solution of the pressure correction equation for three-dimensional flows in complex geometries, both with iterative and direct solvers, are analysed. In particular is shown, through numerical tests, that an iterative solver is incapable to provide an accurate solution due to the ill-conditioning of the pressure correction equation and that its crisis becomes more evident with higher-order convection methods, when using flux limiters or when Dirichlet boundary condition are imposed, while a direct solver can provide an extremely accurate solution without an excessive increase, or even with a reduction, of the computational time required.