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**Two-phase convection in icy satellites.**
*(English)*
Zbl 1267.85002

Summary: Space missions to Jupiter and Saturn provided first estimates of the inner structure of their icy moons and, for some of them (Titan, Europe, Enceladus) suggested the presence of subsurface liquid water reservoirs. Similar subsurface oceans have probably been present in the interior of each differentiated icy satellite, at least at some instant during its evolution. Due to the presence of both water phases and possibly other tracers (methane, ammonium etc.) the proper physical description of these satellites requires the traditional thermal convection approach to be generalized to capture the multicomponent interaction. We present a set of equations derived from the principles of continuum thermodynamics which govern the flow of a two-phase material. Employing the dimensional analysis we identify the leading order terms and arrive at a reduced system of equations that can be compared with other formalisms. To gain some insight into this highly complex system we first focus on a 1D Cartesian case where most of the interaction phenomena characteristic of a two-phase system (porosity shock waves, material singularities. etc.) are already present. The numerical treatment of this basic case already requires advanced numerical techniques (TVD schemes) and serves as a good starting point for further computations involving more realistic scenarios.