A poro-visco-elastodynamic model in Eulerian formulation, its analysis, implementation, and application to phase transitions in the hydrated Earth's mantle

A rather general-purpose poro-visco-elastodynamic model for compressible porous-like media at finite strains in Eulerian formulation in a prescribed gravitational field is studied. The mathematical analysis of the existence of weak solutions is based on a fully-implicit regularized time discretization, which is shown to be numerically stable for sufficiently small time steps and, in a multipolar variant, convergent in terms of subsequences. Applications to geophysical modelling of dehydration of descending wetted slabs or ascending plumes undergoing a volumetric phase transition at the interface between the upper and the lower mantle at 660,km depth, based on a barotropic viscoelastic fluid, are outlined. Implementation aspects via a standard finite element approach are outlined and some 2D computational experiments that highlight some aspects of this compressible geophysical model are presented.