This brief report expresses the basic equations of an incompressible flow model in a form which can be translated easily into the form used by a numerical solver. The application of tensor notation makes is possible to effectively address the issue ofnumerical robustness and stating the model equations on a general form which accommodate curvilinear coordinates. Strong conservation form is obtained by formulating the equations so that the flow variables, velocity and pressure, are expressed in thephysical coordinate system while the location of evaluation is expressed within the transformed coordinate system. The tensor formulation allows both a finite difference and a pseudo-spectral description of the model equations. The intention is for thefinite difference formulation to achieve the same robustness and conservation properties as a finite volume discretization. Furthermore, an invariant form of the equations is included which allows for special solutions to be developed in the transformedcoordinate system. Examples of applications are atmospheric flows over complex terrain, aerodynamically flows, industrial flows and environmental flows.