The present work consists in the development of a numerical method of solution of compressible and incompressible fluid flow for all speed in iregular geometries. A boundary-fitted two-dimensional nonorthogonal curvilinear coordinate systeam is utilized. The cartesian velocity components are the dependent variables in the momentum equations and covariant velocity components are used in the continuity equation. The finite-volume technique was selected to discretuze the steady-state physical phenomenon conservation equations, since this method keeps the conservative property of the equations and its physical consistency in the numerical process. A nonstaggered grid was employed, and all dependent variables are evaluated at the cell center points, which divides the physical domain. The convection-diffusion fluxes at the control volumes faces are evaluated with the Power Law and Quick shemes. Special attention is paid to the numerical treatment of boundary conditions. The problem of velocity-pressure-density coupling is solved using a combination of continuity, momentum equations and state equation resulting in two pressure correction equations. The first equation corrects the density and the pressure, the second equation corrects the mass flux and the velocity. A modification in the velocity correction equations is proposed using a compensationterm to accelerate the convergence. Several types of interpolation of the face density are used to reduce variable atenuations, caused by false diffusion. For the solution of the resulting algebric equations,the line-by-line TDMA algorith is used as well as a block-correction method to accelerate the convergence. The proposed method is verified on six test problems,by comparing the present results with analytical and numerical results avaiable in the literature.