Ascent of Bubbles in Magma Conduits Using Boundary Elements and Particles

We investigate the use of the Multipole-accelerated Boundary Element Method (BEM) and of the Singularity Method for studying the interaction of many bubbles rising in a volcanic conduit. Observation shows that the expression of volcanic eruption is extremely variable, from slow release of magma to catastrophic explosive manifestation. We investigate the application of the Fast Multipole Method to the solution of (i) the Boundary Element Formulation of the Stokes flow and of (ii) the particle formulation using the Stokeslets, the Green Function of the Stokes flow law, as a particle kernel. We show how these implementations allow for the first time to numerically model in a dynamic setting a very large number of bubbles, i.e few thousands with the BEM models, allowing investigating the feedback between the single bubble deformation and their collective evolution, and few hundred of thousands of bubbles with the particle approach. We illustrate how this method can be used to investigate the intense interaction of a large number of bubbles and suggest a framework for studying the feedback between many bubbles and a complex thermal nonlinear magmatic matrix.