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

岩浆从地球内部的产生和分离涉及到各种长度尺度上的相互作用的物理过程。为了更好地了解熔体迁移过程中的异质性和多尺度地幔，促进跨学科的研究和教育，CMG研究项目，建立在现有的优势和资源的应用数学和地质科学部门在布朗大学提出。该项目将侧重于四个密切相关的主题：（1）多组分、粘性变形、具有尖锐界面的多孔介质中反应溶解的理论和数值研究;（2）发展解决多维和多尺度地质问题的数值方法;（3）发展多尺度模型，研究会聚和发散板边界的部分熔融、熔体输送和熔体-岩石反应;（4）与地球化学和地球物理观测的对比。稳定性分析和数值计算，采用自适应间断伽辽金有限元方法将被用来研究地幔中的高孔隙度熔体通道的形成。将非均匀多尺度方法（HMM）与间断方法和有限体积方法相结合，用于研究大尺度岩浆运移过程。一个双孔隙度模型也将开发一个粘性变形的双孔隙介质与渗透率张量，和质量，动量和能量之间的高孔隙度通道和低孔隙度矩阵的传递率由理论和数值计算确定。新一代模型将为理解从毫米到数百公里的长度尺度上的地球化学和地球物理观测建立一个框架。 提出的理论和数值的发展，以自己的方式具有挑战性，是有用的一系列实际应用远远超出地球科学。这项研究的结果将为不同的数学家，地球化学家和地球化学家提供有价值的信息，促进应用数学和地球科学的跨学科整合。这项建议的跨学科性质将对布朗大学的研究生和本科生教育产生重大影响。来自两个部门的研究生和本科生将有机会参与广泛的多学科研究和教育活动。像这样的项目将创造一个环境，培养新一代的科学家，他们具有广泛的多学科技能，能够从过去更具体的学科成果中获得新的理解。

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.