The motion of water in a complex hydrodynamic configuration is characterized by a wide spectrum of space and time scales, due to the coexistence of physical phenomena of different nature. Consequently, the numerical simulation of a hydrodynamic system of this type is characterized by a large computational cost. In this paper, after providing a quite general setting for model coupling, we introduce a first possible technique to reduce such a computational effort, by suitably coupling different hydrodynamic models, namely a dimensionally heterogeneous–physically homogeneous coupling strategy, driven by a priori physical considerations. The aim of this paper is to investigate in more detail the range of reliability of this approach moving from suitable test cases. A second strategy, based on a dimensionally homogeneous–physically heterogeneous coupling, will be provided in the second part of this work [Miglio et al., Proceedings of the Fourth World Congress of Nonlinear Analysis WCNA-2004, Orlando, FL, USA, 2004, accepted for publication].