A numerical formulation to solve the ALE Navier-Stokes equations applied to the withdrawal of magma chambers

Resumen

This thesis presents a numerical formulation to solve the Navier-Stokes equations with mechanical coupling in the context of a Finite Element Method. The solution of the ALE Navier-Stokes equations is based on a fractional step method combined with a pressure gradient projection technique that produces the required stabilisation of the pressure field when implicit versions of the algorithm are considered. The algorithm deals simultaneously with both compressible and incompressible flows using the same interpolation spaces for the pressure and the velocity fields. Fluid-structure interaction problems are solved by means of a staggered procedure in which the fluid and the structural equations are alternatively integrated in time by using separate solvers. A remeshing strategy with a conservative interpolation of nodal variables is also developed. Particular applications are addressed concerning the modelling of the dynamics of magma withdrawal from crustal reservoirs. A physical model for the most common types of (explosive) volcanic eruptions is proposed. Several simulations of eruptive events, ranging from volatile oversaturation driven eruptions to caldera-forming eruptions, are presented. On the other hand, a numerical procedure to compute viscoelastic ground deformations in volcanic areas is also proposed. This procedure is based on the correspondence principle combined with the Laplace transform inversion by means of the Prony series method. It allows to constrain the domain of applicability of the analytical procedures used nowadays and, simultaneously, allows to contemplate a wider spectrum of possibilities such as, for instance, extended sources, topographic effects or anisotropies of the crust.