contravariant velocoties

John

Contravariant velocities are normally used in the pressure based finite volume methods (staggered and colocated grids). This looks more appropriate especially while applying boundary conditions like inlet, exit, wall, symmetry and periodic for irregular geometries.

Generally contravariant velocities are not (mentioned) used in density based finite volume methods. Why?. For irregular geometries, is it not more meaningful to use contravariant velocities while applying the boundary conditions. Or is it done but never mentioned. What is the physical meaning of contravariant velocity I will be extremely happy if these can be clarified Thank you John