CMG Research: Robust Numerical Methods for Multi-Phase Darcy-Stokes Flow in Heterogeneous and Anisotropic Partially Molten Materials

CMG 研究：非均质和各向异性部分熔融材料中多相达西-斯托克斯流的鲁棒数值方法

• 批准号: 1025321
• 负责人: Marc Hesse
• 金额: $ 34.98万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2015-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1025321&HistoricalAwards=false
• 关键词: CMG; Research; Robust; Numerical; Methods

Partial melting and melt segregation is a fundamental process in the interior of the Earth and other planetary bodies. In the Earth it leads to the formation of the oceanic crust at mid-ocean spreading centers and the continental crust above subduction zones, and is therefore an important process creating the large scale compositional heterogeneity of the Earth. Partially molten materials are porous media in which phase equilibrium, heat transfer, and mechanical deformation are tightly coupled by multi-phase flow. Two challenges in modeling these systems are: (1) The non-linear coupling between the viscous flow of the creeping mantle and the porous flow of the melt and other volatiles, i.e., multi-phase Darcy-Stokes flow; and (2) The pervasive heterogeneity and anisotropy of all geological materials that will determine the extent of partial melting and the pathways of melt segregation. The main goal of this interdisciplinary project is to develop robust numerical methods that allow the solution of realistic problems in the geosciences.In the last 30 years, mathematical formulations for multi-phase Darcy-Stokes flow have been developed in geophysics and glaciology, while robust numerical methods for heterogeneous and anisotropic multi-phase systems have been developed for the simulation of geothermal and hydrocarbon reservoirs. This proposal will extend current capabilities in three areas: 1) Extension of the mathematical description to the dynamics of three-phase flow in partially molten systems with an additional fluid phase in the pore space, to allow self-consistent modeling of volatile induced melting in subduction zones. This requires the coupling of both the two-phase Darcy-Stokes equations for the partially molten material with the Buckley-Leverett theory used in multi-phase flow in porous media. 2) The development and analysis of a robust mixed finite element discretization for the multi-phase Darcy-Stokes system that describes partially molten porous media. These methods have been successful, in both limiting cases: heterogeneous and anisotropic Darcy flow as well as incompressible Stokes flow. Mixed methods allow discretely conservative computations of the fluxes that are essential for reactive transport. 3) The development of a reactive transport model for partially molten systems and the analysis of chromatography in partially molten materials. High temperatures allow chemical reactions to remain close to equilibrium, but also make it necessary to treat the liquids as well as the solid as solutions. Partially molten systems are therefore best modeled using techniques for multi-phase flow with phase equilibrium.

部分熔融和熔融分离是地球和其他行星内部的基本过程。 在地球内部，它导致洋中扩张中心洋壳和俯冲带以上陆壳的形成，是造成地球大尺度成分不均匀性的重要过程。 部分熔融材料是多孔介质，其中相平衡、传热和机械变形通过多相流动紧密耦合。 模拟这些系统的两个挑战是：（1）蠕动地幔的粘性流动与熔体和其他挥发物的多孔流动之间的非线性耦合，即，多相Darcy-Stokes流;（2）所有地质材料普遍存在的非均匀性和各向异性，决定了部分熔融的程度和熔体偏析的途径。这个跨学科项目的主要目标是开发强大的数值方法，使地球科学中的现实问题的解决方案。在过去的30年里，多相达西-斯托克斯流的数学公式已经在地球物理学和冰川学，而强大的数值方法的非均质和各向异性多相系统已经开发的地热和油气藏的模拟。该提案将在三个方面扩展当前的能力：1）将数学描述扩展到在孔隙空间中具有额外流体相的部分熔融系统中的三相流的动力学，以允许俯冲带中的挥发性诱导熔融的自洽建模。这就需要耦合的两相Darcy-Stokes方程的部分熔融材料与Buckley-Leverett理论用于多相流在多孔介质中。 2)描述部分熔融多孔介质的多相Darcy-Stokes系统的鲁棒混合有限元离散的发展和分析。这些方法在两种极限情况下都是成功的：非均质和各向异性达西流以及不可压缩斯托克斯流。 混合方法允许离散保守计算的通量是必不可少的反应运输。3)部分熔融体系反应输运模型的建立和部分熔融材料的色谱分析。高温允许化学反应保持接近平衡，但也使得有必要将液体和固体作为溶液处理。 因此，部分熔融系统最好使用具有相平衡的多相流技术来建模。

项目成果

Percolative core formation in planetesimals enabled by hysteresis in metal connectivity

• DOI: 10.1073/pnas.1707580114
• 发表时间: 2017-12-19
• 期刊: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• 影响因子: 11.1
• 作者: Ghanbarzadeh, Soheil;Hesse, Marc A.;Prodanovic, Masa
• 通讯作者: Prodanovic, Masa

Reactive transport in a partially molten system with binary solid solution: MELT TRANSPORT WITH SOLID SOLUTION

具有二元固溶体的部分熔融系统中的反应传输：固体溶液的熔体传输

• DOI: 10.1002/2015gc005956
• 发表时间: 2015
• 期刊: Geosystems
• 作者: Jordan, Jacob S.;Hesse, Marc A.
• 通讯作者: Hesse, Marc A.

A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures

两相混合物产生的线性简并椭圆方程

• DOI: 10.1137/16m1067846
• 发表时间: 2016
• 期刊: SIAM Journal on Numerical Analysis
• 影响因子: 2.9
• 作者: Arbogast, Todd;Taicher, Abraham L.
• 通讯作者: Taicher, Abraham L.

A level set method for materials with texturally equilibrated pores

• DOI: 10.1016/j.jcp.2015.05.023
• 发表时间: 2015-09-15
• 期刊: JOURNAL OF COMPUTATIONAL PHYSICS
• 影响因子: 4.1
• 作者: Ghanbarzadeh, Soheil;Hesse, Marc A.;Prodanovic, Masa
• 通讯作者: Prodanovic, Masa

Percolation and Grain Boundary Wetting in Anisotropic Texturally Equilibrated Pore Networks

• DOI: 10.1103/physrevlett.113.048001
• 发表时间: 2014-07-25
• 期刊: PHYSICAL REVIEW LETTERS
• 影响因子: 8.6
• 作者: Ghanbarzadeh, Soheil;Prodanovic, Masa;Hesse, Marc A.
• 通讯作者: Hesse, Marc A.