Factorized implicit upwind methods applied to inviscid flows at high Mach number

The performance of several approximate factorization methods, coupled with a finite volume spatial discretization using Roe's approximate Riemann solv er, are compared by means of numerical tests on a two-dimensional steady in viscid Row past a blunt body at Mach numbers ranging from 5 to 20, The comp arisons are carried out evaluating, by numerical experiments, the optimal C ourant number of each method. The alternating direction implicit and the lo wer-upper symmetric Gauss-Seidel methods result in the most efficient facto rizations, in terms of CPU time. The former behaves smoothly with increasin g Mach number, and its performance is not affected by the grid size, The la tter may achieve higher efficiency but is strongly dependent on the number of relaxation steps performed, requiring optimization in terms of Mach numb er and grid size.