A poro-visco-elastodynamic model in Eulerian formulation, its analysis, implementation, and application to phase transitions in the hydrated Earth's mantle
Authors
- Peschka, Dirk
ORCID: 0000-0002-3047-1140 - Roubíček, Tomáš
ORCID: 0000-0002-0651-5959
2020 Mathematics Subject Classification
- 76N06 35Q86 86A99 74F10 65M60
Keywords
- Heterogenous compressible continua, geophysical mantle dehydration and 660-km discontinuity, weak solutions and numerics
DOI
Abstract
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.
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