Toward Modeling Lava Breakouts

When molten lava effuses from an active volcano and spreads into the surrounding terrain it immediately begins to cool and degas; this effectively changes the lava's rheology and can cause it to develop a crust that resists the momentum of its spreading. If the crust gets strong enough, the lava will eventually cease to advance; internal pressure will increase as lava continues to effuse from the vent. Over time, this build-up of internal pressure can cause the lava to inflate, and ultimately to "breakout" from its original emplacement and become free to interact with new terrain and spread to areas outside of its initial path.

Any attempt to quantify the risk associated with these breakouts is difficult; to date, no existing flow models include them. Nonetheless, recent advances in observational techniques and the numerical study of differential equations have the laid the ground work for new insight into this phenomenon. Commensurate with this development, we present a three-dimensional lava flow model with a foundation built on experiments and observations, as well as rigorous mathematical theory that aims to predict the spatial and temporal dynamics of lava breakouts. The model's mathematical formulation is built on a simplified version of the Navier-Stokes equations and makes use of dynamic boundary conditions and effusion rates that allow the lava flow to emplace, inflate and evolve organically. Numerically, the model utilizes novel discontinuous Galerkin (DG) finite element methods that leverage high-order integration techniques to accurately calculate pressure gradients and resolve terrain variations which drive lava advance. Model results are evaluated against analog and molten basalt laboratory experiments as well as natural flow examples, and a path forward in terms of predicting lava breakouts and assessing the risk associated with them is discussed.