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 solver, are compared by means of numerical tests on a two-dimensional steady inviscid Row past a blunt body at Mach numbers ranging from 5 to 20, The comparisons are carried out evaluating, by numerical experiments, the optimal Courant number of each method. The alternating direction implicit and the lower-upper symmetric Gauss-Seidel methods result in the most efficient factorizations, in terms of CPU time. The former behaves smoothly with increasing Mach number, and its performance is not affected by the grid size, The latter may achieve higher efficiency but is strongly dependent on the number of relaxation steps performed, requiring optimization in terms of Mach number and grid size.