Simulation of Multiphase Flow and Transport in the Partially Molten Mantle

University Of Texas At Austin, Austin TX

Investigators

Abstract

Volcanic eruptions affect, for example, local water supplies and the global climate. Volcanism at the Earth's surface is due to partial melting of the convecting mantle, and subsequent segregation of molten rock components. The Earth's mantle is generally below its melting point and thus solid. Partial melting occurs generally in three locations, at mid-ocean ridges where oceanic crust is formed, hot-spots below ocean islands and some continental sites like Yellowstone, and subduction zones where oceanic crust returns to the mantle and continental crust is formed. To better understand volcanic processes, geochemical surface observations must be linked to the composition and distribution of mantle rocks, which are heterogeneous due to incomplete chemical mixing of material during mantle convection. The project will develop numerical models that can resolve the small-scale dynamics of these processes. It is a joint effort of a mathematician and a geoscientist, as well as an undergraduate and a graduate student, who will be educated in an interdisciplinary setting. People so trained are in high demand by industrial and government labs. Project objectives include the development of (1) a mathematical framework for computational simulation of evolving mantle flow which covers the degenerate case of no melt, (2) a numerical method to accurately approximate the transport of temperature and chemical components within the mantle flow, (3) a computer code to implement the flow and transport algorithms, as well as a method for handling simple phase behavior. Furthermore, (4) the code will be applied to study important problems in the geosciences and (5) students will be educated and trained in an interdisciplinary setting. Mathematically speaking, because there are regions with no melt, two-phase flow in the mantle is governed by highly degenerate equations. Recent work has established the mathematical foundations of two-phase flow when the porosity does not evolve. The key is to scale the solution variables and equations appropriately by the porosity, which is the volume fraction of melt. The evolving case will be treated in this project, with the goal of providing an appropriate computational method for simulating the flow in practical simulations. To model the transport of temperature and the segregation of melt components, appropriate WENO and discontinuous Galerkin methods will be developed for this project, which will respect the possible degeneracies in the porosity.