The work of the SIGMA group focuses on better understanding complex multi-phase-flow systems that are fundamental to many questions in Earth science. We pursue this goal by developing original computational methods that are customized for the problem at hand.

An example of the kind of work we do is a code that captures the interface dynamics of large gas bubbles in viscous flow as might arise during degassing in basaltic volcanoes like Stromboli. Our numerical methodology is based on finite differences on a fixed grid that couples three numerical tools – ghost fluids, level sets, and extension velocities – to obtain an accurate and efficient approach. Our simulations show that the current paradigm for normal eruptions at Stromboli, which is based on the idea that each eruption represents gas pockets of several meters in size bursting at the free surface of the fluid magma in the conduit, may be unsatisfactory because the gas pockets are unstable.

One of the fundamental challenges in developing computational tools for Earth systems are the drastic differences in temporal and spatial scales involved. While resolving the dynamics of a planetary-scale process at small scales is prohibitive, assumptions about physical and chemical properties at these scales typically have an important impact on the macroscopic behavior. To derive effective material properties at macroscopic scales from the microscopic properties, we have developed a code that couples the fluid and solid behavior of crystal-bearing fluids based on distributed Lagrange multipliers. Contrary to many other numerical techniques for solid-fluid coupling in which the hydrodynamic forces on the solid bodies are incorporated through approximate drag formulas, our approach fully resolves the flow around each individual solid body without assuming a specific type of drag or lift. This more general approach is particularly advantageous for complex flow problems, for which it is often not possible to specify drag and lift apriori.