Ignorance of mesh dependency can sometimes be an embarrassment in numerical calculations. Mesh structures need to be developed to eradicate mesh dependency without compromising the finite computing resource and/or incurring large computational expense. For the inexperienced, mesh deployment often degenerates into a time-consuming iterative procedure. To understand mesh influences, different mesh-structures have been applied to two simple, yet typical, room-air-ventilation configurations. The predictions, using various mesh regimes, have been compared with a datum result set: marks have been awarded according to the closeness of comparison to mesh-independent predictions. This mark, i.e. the 'Mesh Independence Number' (MIN), is a numerical indicator of the closeness to achieving a mesh in-dependent solution. A relationship for the MIN versus number of nodes is presented together with relationships for the average values of the air-velocity components. In many instances, high correlation-coefficients are established which suggests that this MIN methodology could reduce the need for iterative time-consuming mesh-dependency studies.