SI2-SSE: Development and Implementation of Software Elements using State-of-the-Art Computational Methodology to Advance Modeling Heterogeneities and Mixing in Earth's Mantle

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This project involves the development and implementation of scientific software elements (SSEs), based on modern, high-resolution numerical methods for modeling steep gradients and sharp interfaces of material properties in viscous fluids in the presence of thermal convection. The goal of this project is to address a compelling need in geodynamics, in which continuum mechanics is applied to the study of geophysical processes, such as convection in the Earth?s mantle. A primary tool of geodynamics research is computational models of the flow of the extremely viscous interior of the Earth over hundreds of millions to billions of years. A long-standing challenge for these models is the need to accurately model sharp interfaces in temperature, viscosity, and other properties. These arise when, for example, modeling subduction (in which a cold tectonic plate plunges into the hot interior) or rising plumes (in which a hot boundary layer instability rises through the mantle and encounters the cold boundary layer of the tectonic plates). The project will foster interdisciplinary communication and the application of state-of-the-art applied and computational mathematics to fundamental problems in geophysics. It involves early-career mathematical scientists in the application of state-of-the-art numerical algorithms to geodynamics and, in particular, will provide an opportunity to increase the participation of women in mathematics and geodynamics research.This project involves the design and implementation of state-of-the-art SSEs for computing the evolution of significant processes in the Earth's mantle in which an essential feature of the problem is the presence of one or more moving boundaries, interfaces, or steep gradients in temperature, composition, or viscosity. The SSEs will address two critical issues that currently limit modern mantle convection simulations. All computational models of mantle convection currently in use produce significant overshoot and undershoot in the neighborhood of sharp gradients in temperature and viscosity. The cause of these overshoots and undershoots is a numerical artifact, which is well-known and well-understood in other fields, such as the computational shock physics community. Over the past thirty years researchers in computational shock physics have developed a variety of high-order accurate, monotone numerical methods, which preserve the physically correct maximum and minimum values of the computed quantities, while producing a high-order accurate numerical approximation of these quantities. Another compelling need in computational geodynamics is the ability to track discontinuous jumps in quantities such as material composition. Here high-order accurate interface tracking algorithms are required, since these fields undergo large-scale deformation, yet quantities such as the viscosity must be accurately approximated at the interface between two materials.