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

地球内部岩浆的产生和分离涉及到在大范围长度尺度上相互作用的物理过程。为了更好地理解非均质多尺度地幔中熔体迁移的过程，促进跨学科研究和教育，提出了一项基于布朗大学应用数学和地质科学系现有优势和资源的CMG研究项目。该项目将重点关注四个密切相关的主题：(1)多组分、粘性可变形、具有尖锐界面的多孔介质中反应性溶解的理论和数值研究；(2)多维、多尺度地质问题数值求解方法的发展；(3)建立了部分熔融、熔体输运和熔融岩反应的多尺度模型；(4)与地球化学和地球物理观测的对比。采用自适应不连续Galerkin有限元方法进行稳定性分析和数值计算，研究地幔中高孔隙度熔体通道的形成。非均质多尺度方法（HMM）将与不连续和有限体积方法相结合，用于大长度尺度上岩浆运移过程的研究。对于具有渗透性张量的粘性可变形双孔隙介质，还将开发双孔隙模型，并通过理论和数值计算确定高孔隙度通道和低孔隙度基质之间的质量、动量和能量传递率。新一代的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。所提出的理论和数值发展，以其自身的方式具有挑战性，对远远超出地球科学的一系列实际应用是有用的。这项研究的结果将为数学家、地球化学家和地球物理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。该提案的跨学科性质将对布朗大学的研究生和本科教育产生重大影响。两个系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。拟议中的项目将创造一种环境，培养具有广泛的多学科技能的新一代科学家，他们需要从过去的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.