Numerical model of two-phase magma flow with bubble coalescence
^^Cassandre Lebot^^¹, Alain Burgisser², Christophe Lacave³, Gladys Narbona-Reina⁴, Didier Bresch¹, Marielle Collombet²
Affiliations: ¹ LAMA UMR5127 CNRS, Université Savoie Mont Blanc, Le Bourget du lac, France ² ISTerre CNRS, Université Grenoble Alpes, Université Savoie Mont Blanc, Grenoble, France ³ LAMA UMR5127 CNRS, ISTerre UMR5275 CNRS, Université Savoie Mont Blanc, Le Bourget du lac, France ⁴ Dpto. Matemática Aplicada I E.T.S Arquitectura, Universidad de Sevilla, Sevilla, Spain
Presentation type: Poster
Presentation time: Tuesday 16:30 - 18:30, Room Poster Hall
Poster Board Number: 193
Programme No: 3.2.16
Abstract
We introduce bubble coalescence into a recent conduit flow model that ensures the conservation of mass and volatile species and the dissipation of total energy. It extends the capability of this two-phase (gas and silicate melt) model to simulate some eruptive regimes (e.g., Strombolian) that are controlled by coalescence processes, which can help us to better understand these eruptive dynamics. Using kinetic theory, which tracks the number of bubbles in a microscopic volume of magma, we relax the assumption of a constant bubble number density and determine how to introduce bubble coalescence at a microscopic level. We then obtain a macroscopic description of coalescence that is compatible with the original, averaged two-phase flow model. While this original model has eight transport equations on eight unknowns (gas volume fraction and density, dissolved water content, liquid pressure, and the velocity and temperature of both phases), we obtain two more transport equations for bubble radius and bubble number density, respectively. We establish the energy balance of our updated model and find how bubble coalescence contributes to the dissipation of total energy. Finally, we solve our new system numerically with different rates of coalescence and compare the numerical outputs to those of the model without bubble coalescence.