The finer the mesh the lower the Péclet number. As a very rough rule of thumb the literature often said that the grid Péclet number should not exceed a value of 2. From my experience, I do not always insist to satisfy a number smaller than 2. Other factors as such as the type of physical problem (e.g. linear non-linear), the degree of required accuracy, computational resources may also play a role in the mesh design. Anyway, the Péclet provides a useful quantitative measure on whether or not the mesh is fine enough for a transport model.
