CMG: Developing a Multiscale Model for Melting and Melt Migration in the Mantle

点击翻译按钮获取中文摘要

The generation and segregation of magma from the Earth's interior involves interacting physical processes on a wide range of length scales. To better understand the processes of melt migration in a heterogeneous and multiscale mantle and to promote interdisciplinary research and education, a CMG research project that builds around the existing strengths and resources of the Applied Math and Geological Sciences departments at Brown University is proposed. The project will focus on four closely related themes: (1) theoretical and numerical studies of reactive dissolution in multicomponent, viscously deformable, porous media with sharp interfaces; (2) development of numerical methods for solving multi-dimensional and multiscale geologic problems; (3) development of multiscale models for studying partial melting, melt transport and melt-rock reaction at converging and diverging plate boundaries; and (4) comparison with geochemical and geophysical observations. Stability analysis and numerical calculations using adaptive discontinuous Galerkin finite element methods will be used to study the formation of high porosity melt channels in the mantle. The heterogeneous multiscale method (HMM) coupled with discontinuous and finite volume methods will be developed for studying magma transport processes on large length scales. A double porosity model will also be developed for a viscously deformable duo-porosity medium with permeability tensors, and mass, momentum, and energy transfer rates between the high porosity channels and the low porosity matrices being determined by theoretical and numerical calculations. This new generation of models will establish a framework for understanding geochemical and geophysical observations over length scales ranging from millimeters to hundreds of kilometers. The proposed theoretical and numerical developments, challenging in their own way, are useful to a range of practical applications far beyond the Earth Sciences. Results from this study will provide valuable information for a diverse group of mathematicians, geochemists, and geophysicists, promoting cross-disciplinary integration in applied math and Earth Sciences. The interdisciplinary nature of this proposal will have a great impact on graduate and undergraduate education at Brown University. Graduate and undergraduate students from both Departments will have the opportunity of involvement in a broad multidisciplinary research and educational activities. Projects like the one proposed will create an environment in which to train a new generation of scientists with the broad multidisciplinary skills needed to derive new understanding from the more discipline specific results of the past.