Study of Europa's crust via a Stefan model with convection

We present results of a numerical simulation of the thermal convection in the subsurface mushy ice layer of Europa, one of the Jupiter's moons. Beside fluid dynamics and heat transfer within such a layer, heat conduction in the solid crustal surface and heat exchange between the two phases - mushy ice and solid crust - are included in our model in order to follow also the evolution of the phase front. Since the images of Europa's crust taken by the spacecrafts Voyager and Galileo got to be known, planetary scientists stimulated this kind of investigations with the aim of studying the origin of such a topographic aspect. Actually the chaotic lineaments and splotches, clearly visible, solicited the conjecture of the existence of an internal ocean of water that is also supported by the most recent Galileo magnetic field data. The presence of water would make life possible on the jovian satellite. However, in the recent literature, just few numerical simulations describing the overall scenario and including either heat transfer and convection flow have been proposed. Here we adopt the stream-function/vorticity formulation of the Navier-Stokes equations for the flow of the mushy ice and a Stefan condition combined with a front-fixing technique for the front evolution. Our numerical discretization is based upon an ENO scheme. Mathematical model and numerical procedure have been thoroughly tested and have the advantage of yielding accurate numerical solutions via relatively coarse space discretization grids. For applications in this field the present one is the first attempt, at our knowledge, to solve a complete Stefan condition with convection flow, obtaining a good match with other numerical solutions in the literature.