Azonal-local solution method is developed for the solution of the compressible Navier-Stokes equations. The main feature of the method is coupling of the Navier- Stokes equations with the Euler equations and the local mesh solution procedure. Mesh sequencing (multilevel) technique is also used for the improvement of the efficiency of the algorithm. The methodology is applied to turbulent flowfields past an airfoil. A flux vector splitting method with an upwind scheme up to fourth-order accuracy is used for the discretization of the inviscid fluxes. The system of the equations is solved by an unfactored implicit method using Gauss-Seidel relaxation.