Lattice Boltzmann Methods for Concentration- and Temperature-Induced Density Driven Flows

晶格玻尔兹曼方法（lbm）的最新进展为解决浓度和温度诱导的密度驱动流的非线性问题提供了一种全新的计算方法。沿海地区地下水流动中低密度淡水和高密度海水之间的相互作用说明了一般问题的性质。沿海地区的地下水模型必须能够模拟密度驱动的流动以及多孔介质中溶质和热量的耦合平流、扩散和分散。尽管加快简单比传统(如有限元)方法对于这些问题,他们之前从未被应用到海水入侵问题。由于涉及非线性、耦合溶质/能量输运和密度驱动流动的传统模拟固有的数值困难，文献中经常报道不一致的数值结果。这些模型所处理的问题的解析解很少可用，而且各种代码的“验证”通常依赖于与先前数值结果的比较。作为一种完全不同的、更基本的方法，lbm可能对澄清这些问题作出重大贡献，并提供一种更有力、更有效的解决这些问题的方法。我们将比较LBM与处理基准问题的传统方法，并为更大的实际问题开发代码。这项研究对于提高对沿海含水层、其他受盐影响的含水层和高水平（热）废物处理的认识和理解至关重要。流体和多孔介质的其他重要学科可能会受益。PI和研究团队是唯一有资格进行这个项目的人。PI进行了溶质迁移、孔隙和宏观尺度分散以及lbm的研究。研究团队包括一位精通lbm、数值方法和并行算法的计算机科学家。有充足的资源可用于实施该项目（见支持信）。更广泛的影响拟议的工作将为初级PI，博士后研究员，研究生和本科生提供lbm和现有模型的丰富经验。博士后和学生将接受强化培训。该项目将直接提高FIU学生的课堂和研究经验，FIU拥有卡内基基金会最高的评级（博士/研究型大学-广泛），是公认的少数民族服务机构，向西班牙裔学生颁发的学士学位比任何其他美国大学都多。未来的博士后和研究生将受益。项目参与者之间将建立终身科学伙伴关系。开设高级溶质输运建模新课程。本科生将从FIU的NSF GeoSCOPE项目中招募（见支持信）。高性能计算和算法开发工作将为广泛的科学界带来永久性的基础设施增强和建模工具。研究结果将以评审期刊文章、科学会议报告、论文和互联网的形式广泛传播。软件将提供给感兴趣的研究人员，并最终作为一个模块化的选项，从广泛使用的模型接口访问。社会将受益于科学家和工程师能力的增强，从而更准确、更迅速地预测由溶质浓度和温度变化引起的密度驱动的水流，这些变化影响着沿海地区数百万依赖地下水的人。

0440253SukopRecent advances in lattice Boltzmann methods (LBMs) offer a radical new way of computing solutions to the challenging non-linear problems of concentration- and temperature-induced density driven flows. Interactions between low density fresh water and high density seawater in ground water flows in coastal regions illustrate the nature of the general problem. Ground water models for coastal areas must be able to simulate density driven flow and the coupled advection, diffusion, and dispersion of solutes and heat in porous media. Although LBMs are simpler than conventional (e.g., finite element) methods for these problems, they have not previously been applied to seawater intrusion problems. Because of the numerical difficulties inherent in conventional simulations involving non-linear, coupled solute/energy transport and density-driven flow, inconsistent numerical results have often been reported in the literature. Analytical solutions for the problems addressed by these models are rarely available, and 'validation' of various codes has generally relied on comparison with previous numerical results. As a completely different, more fundamental approach, LBMs may contribute significantly to clarifying these issues and offer a more robust and efficient means of solving these problems. We will compare LBM with conventional approaches for benchmark problems and develop code for larger, realistic problems.Intellectual merit of the proposed activityThis research is critical to advancement of knowledge and understanding of the hydrology of coastal aquifers, other salt-affected aquifers, and high-level (hot) waste disposal. Other disciplines where fluids and porous media are important could benefit.The PI and research team are uniquely qualified to conduct this project. The PI has conducted research on solute transport, pore- and macro-scale dispersion, and LBMs. The research team includes a computer scientist with expertise in LBMs, numerical methods, and parallel algorithms. Ample resources are available to conduct the project (see letters of support).Broader ImpactsThe proposed work will provide the beginning PI, the post-doctoral researcher, and graduate and undergraduate students with extensive experience in LBMs and existing models. The post-doc and students will receive intensive training. The project will lead directly to enhanced classroom and research experiences for students at FIU, which holds the Carnegie Foundation's highest rating (Doctoral/Research University-Extensive) and is a recognized Minority Serving Institution that awards more Bachelor's degrees to Hispanic students than any other U.S. university. Future students of the post-doc and graduate student will benefit. Career-long scientific partnerships will be established between the project participants. A new course in advanced solute transport modeling will be developed. Undergraduates will be recruited from the NSF GeoSCOPE project at FIU (see letter of support). The high-performance computing and algorithm development work will result in permanent infrastructure enhancement and modeling tools for the broad scientific community. Results will be broadly disseminated as refereed journal articles, presentations at scientific meetings, a dissertation, and via the Internet. Software will be available to interested researchers and ultimately as a modular option accessible from widely used model interfaces. Society will benefit from the enhanced ability of scientists and engineers to more accurately and rapidly predict density-driven flows arising from solute concentration and temperature variations such as those that affect millions of people who depend on ground water in coastal areas.