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

CMG：开发地幔熔融和熔融迁移的多尺度模型

• 批准号: 0530862
• 负责人: Yan Liang
• 金额: $ 88.06万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0530862&HistoricalAwards=false
• 关键词: CMG; Developing; Multiscale; Model; Melting

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.

地球内部岩浆的产生和分离涉及各种长度尺度上相互作用的物理过程。为了更好地了解异质和多尺度地幔中的熔体迁移过程，并促进跨学科研究和教育，提出了一个围绕布朗大学应用数学和地质科学系现有优势和资源建立的 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溶解的理论和数值研究； （2）发展解决多维、多尺度地质问题的数值方法； (3) 开发多尺度模型，用于研究会聚和发散板块边界处的部分熔融、熔体输运和熔岩反应； (4) 与地球化学和地球物理观测结果的比较。使用自适应间断伽辽金有限元方法进行稳定性分析和数值计算将用于研究地幔中高孔隙率熔体通道的形成。将开发与不连续和有限体积方法相结合的异质多尺度方法（HMM），用于研究大长度尺度上的岩浆输送过程。还将开发用于粘性可变形双孔隙介质的双孔隙模型，其具有渗透率张量，以及通过理论和数值计算确定的高孔隙率通道和低孔隙率基质之间的质量、动量和能量传递率。新一代模型将建立一个框架，用于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。 所提出的理论和数值发展虽然以其自身的方式具有挑战性，但对于地球科学之外的一系列实际应用很有用。这项研究的结果将为不同的数学家、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生教育产生巨大影响。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。像所提议的项目将创造一个环境，培养新一代科学家，使他们具备广泛的多学科技能，从过去更具体的学科成果中获得新的理解。