Data-driven stochastic analysis of flow in random heterogeneous media

随机异质介质中流动的数据驱动随机分析

基本信息

  • 批准号:
    0809062
  • 负责人:
  • 金额:
    $ 25.2万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2008
  • 资助国家:
    美国
  • 起止时间:
    2008-08-15 至 2012-07-31
  • 项目状态:
    已结题

项目摘要

This proposal concerns the analysis of transport phenomena in heterogeneous random media with emphasis on the multi-length scale variations in properties that these phenomena exhibit, and the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. The non-intrusive stochastic multiscale framework being developed has three key components: (a) A computational framework that encodes the limited information available about the variability of the (multiscale) material properties (permeability) into a reduced-order stochastic input model, (b) An adaptive sparse grid collocation framework for solving the stochastic PDEs involved and (c) A mathematically consistent strategy to exchange information across length scales for the solution of stochastic multiscale problems. The key concept explored in the data-driven reduced-order stochastic input model construction is the low-dimensional parametrization of manifolds embedded in high-dimensional spaces. The sparse grid collocation approach constructs the stochastic solution solely based on function calls to the corresponding deterministic physical simulator. The framework is based on hierarchical basis functions in multiple dimensions. Adaptivity and convergence are ensured by utilizing a local support while scalability is guaranteed by the careful choice of appropriate data structures. The information transfer strategies are based on the decoupled structure of the stochastic and multiscale algorithms. The results of this research will impact the understanding of flow processes in random media. Thermal and hydrodynamic transport in random heterogeneous media are ubiquitous processes occurring in various scales ranging from the large scale (e.g. geothermal energy systems, oil recovery, geological heating of the earth?s crust) to smaller scales (e.g. heat transfer through composites, polycrystals, flow through pores, inter-dendritic flow in solidification, heat transfer through fluidized beds). There has been increasing scientific, technological and economic interests in predictive modeling of the thermal and hydrodynamic behavior of such media. In addition, this work can be valuable in understanding other systems that are poorly understood and/or controlled due to the gappy and inaccurate data available for their description. The problems addressed provide a unique and valuable training opportunity for students to learn, develop and apply cutting edge computational mathematics techniques to a variety of complex systems.
这个建议涉及的非均质随机介质中的传输现象的分析,重点是这些现象表现出的多长度尺度的属性变化,以及固有的有限的信息,可用于量化这些属性的变化,有必要把这些现象作为随机过程。 正在开发的非侵入式随机多尺度框架有三个关键组成部分:(a)一个计算框架,它对关于气候变化的有限信息进行编码,(多尺度)材料特性(渗透性)到降阶随机输入模型中,(B)用于求解所涉及的随机偏微分方程的自适应稀疏网格配置框架,以及(c)一个数学上一致的策略,以交换跨长度尺度的随机多尺度问题的解决方案的信息。 在数据驱动的降阶随机输入模型构造中探索的关键概念是嵌入在高维空间中的流形的低维参数化。稀疏网格配置方法仅基于对相应的确定性物理模拟器的函数调用来构造随机解。该框架是基于多个维度的分层基函数。通过利用本地支持来确保自适应性和收敛性,同时通过仔细选择适当的数据结构来保证可扩展性。信息传递策略是基于随机和多尺度算法的解耦结构。 这项研究的结果将影响随机介质中流动过程的理解。随机非均质介质中的热动力输运是一个普遍存在的过程,从大尺度(如地热能系统、石油开采、地球地质加热?(例如,通过复合材料的传热、多晶体的传热、通过孔隙的传热、凝固过程中的枝晶间流动、通过流化床的传热)。对这种介质的热和流体动力学行为的预测建模已经引起越来越多的科学、技术和经济兴趣。此外,这项工作可以是有价值的,在了解其他系统的理解和/或控制,由于其描述的差距和不准确的数据。所解决的问题提供了一个独特的和宝贵的培训机会,让学生学习,发展和应用尖端的计算数学技术,以各种复杂的系统。

项目成果

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Nicholas Zabaras其他文献

A thermomechanical study of the effects of mold topography on the solidification of Aluminum alloys
  • DOI:
    10.1016/j.msea.2005.05.046
  • 发表时间:
    2005-09-15
  • 期刊:
  • 影响因子:
  • 作者:
    Lijian Tan;Nicholas Zabaras
  • 通讯作者:
    Nicholas Zabaras

Nicholas Zabaras的其他文献

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{{ truncateString('Nicholas Zabaras', 18)}}的其他基金

A data-driven Bayesian framework for the solution of SPDEs on random heterogeneous media
随机异构介质上 SPDE 求解的数据驱动贝叶斯框架
  • 批准号:
    1214282
  • 财政年份:
    2012
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Standard Grant
Support for US Participants in the USA/South American Symposium on Stochastic Modeling and Uncertainty Quantification in Complex Systems; Rio de Janeiro, Brazil; August 1-5, 2011
支持美国/南美复杂系统随机建模和不确定性量化研讨会的美国参与者;
  • 批准号:
    1068311
  • 财政年份:
    2011
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Standard Grant
On the Design of Polycrystalline Materials with an Integration of Multiscale Modeling and Statistical Learning
多尺度建模与统计学习相结合的多晶材料设计
  • 批准号:
    0757824
  • 财政年份:
    2008
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Standard Grant
Development of a Robust Computational Design Simulator for Industrial Deformation Processes
开发工业变形过程的鲁棒计算设计模拟器
  • 批准号:
    0113295
  • 财政年份:
    2001
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Continuing grant
On the Design of Bulk Forming Processes
批量成形工艺设计研究
  • 批准号:
    9522613
  • 财政年份:
    1995
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Continuing Grant
Inverse and Design Thermomechanical Problems in Solidification Processing
凝固过程中的反演和设计热机械问题
  • 批准号:
    9115438
  • 财政年份:
    1992
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Continuing grant
Presidential Young Investigator Award: Inverse and Design Problems in Manufacturing
总统青年研究员奖:制造中的逆向和设计问题
  • 批准号:
    9157189
  • 财政年份:
    1991
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Continuing Grant
Fixed Domain and Deforming FEM Techniques as Applied to Some Inverse Solidification Problems
固定域和变形有限元技术在某些逆凝固问题中的应用
  • 批准号:
    8802069
  • 财政年份:
    1988
  • 资助金额:
    $ 25.2万
  • 项目类别:
    Standard Grant

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