Numerical modeling of complex geometries necessitates the use of curvilinear body fitted coordinates. This article proposes a novel mixed basis formulation of the governing conservation equations for general curvilinear non-orthogonal grids with the physical covariant velocity as the primary solution variable. This results in an algorithm which has many advantages of orthogonal equations. The conservation equations written in this form retains the diagonal dominance of the pressure equation. The newly formed conservation equations are solved on a structured grid using the SIMPLER algorithm and are shown to converge well for non-orthogonal grids. Standard K–ϵ model is used for the turbulence closure.