AbstractA method to solve the incompressible Navier-Stokes equations for irregular three-dimensional geometries is developed. The method consists of two stages. The first stage involves a coordinate transformation that regularizes the awkwardly shaped surfaces into planar ones by suitably stretching or“ironing out”uneven surfaces. This change of coordinates converts the physical space into a transformed space, which forms, in general, a nonorthogonal curvilinear system. The resulting Navier-Stokes equations now involve a few additional nonlinear terms but the boundary conditions can now be applied very simply and accurately. The boundary layers near the surface are resolved through the second stage involving another coordinate transformation such that only the boundary layers are broadened without substantially affecting the interior region. This transformation from the transformed space of the first stage to the computational space is orthogonal and results in a concentration of grids near the boundaries only. All of the basic mathematical formulations are given in this paper.