An efficient implicit method for the computation of steady three-dimensional (3D), compressible Navier-Stokes equations is presented. In the framework of the backward-Euler scheme, different splitting of an unfactored upwind implicit matrix are used to define different relaxation methods. Either an alternation of LU-type relaxation sweeps or the most efficient LU-type relaxation sweep is used to drive the solution towards steady-state. Centred flux formula plus matrix dissipation is considered for the discretization of mean flow convective flux. Convergence rates are studied for two 3D test cases, which illustrate the efficiency of the numerical schemes.

implicit scheme, compressible flows, turbulent flows, relaxation, implicit stage.