Theses lectures will serve as an introduction to and description of simple examples of kinetic regimes in the modeling of channel flow in a highly dopped region. The focus will be on the transport scales due both to channel geometrical constraints as well as to boundary conditions. These changes of scale will provide simple examples of non-equilibrium regimes and demonstrate the need to investigate their corresponding hydrodynamic approximations, and their transitional kinetic-fluid interfaces. We shall discuss some issues related to the simulation of these transitional regimes, some examples of hybrid computational strategies that take into account scaling-domain decompositions and make comparisions to classical simulations.

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