The numerical solution of the steady two-dimensional Euler and Navier-Stokes equations using unstructured meshes with triangular elements is considered. A finite volume vertex-centered scheme is used. The Roe upwind scheme is implemented for the inviscid fluxes calculation, coupled with a monotonic extrapolation scheme (MUSCL) for higher-order accuracy. Viscous fluxes are calculated via a finite-element consistent scheme. The discretized equations are solved by means of a point-Jacobi procedure and the algorithm is ported on a distributed memory computer. The recursive spectral bisection algorithm provides patched or overlapping subdomains which are assigned to different processors. Overlapping or non-overlapping subdomain solutions are compared in terms of (a) computer cost for the partitioning, (b) efficiency of the parallel processing of the flow equations and (c) susceptibility of artifices for improving speed-up. The numerical solution of the steady two-dimensional Euler and Navier-Stokes equations using unstructured meshes with triangular elements is considered. A finite volume vertex-centered scheme is used. The Roe upwind scheme is implemented for the inviscid fluxes calculation, coupled with a monotonic extrapolation scheme (MUSCL) for higher-order accuracy. Viscous fluxes are calculated via a finite-element consistent scheme. The discretized equations are solved by means of a point-Jacobi procedure and the algorithm is ported on a distributed memory computer. The recursive spectral bisection algorithm provides patched or overlapping subdomains which are assigned to different processors. Overlapping or non-overlapping subdomain solutions are compared in terms of (a) computer cost for the partitioning, (b) efficiency of the parallel processing of the flow equations and (c) susceptibility of artifices for improving speed-up.