Collaborative Research: Efficient Lattice Boltzmann Methods for Multiphase and Multicomponent Flows

多相和多组分流动的高效晶格玻尔兹曼方法本提案的总体目标是通过专门为此类问题设计的高效晶格玻尔兹曼方法的制定、实施和验证，推进多相和多组分流动的最新数值模拟。晶格玻尔兹曼方法是基于动力学理论的介观方法，在相空间的粒子分布函数水平上进行操作。这些方法特别适合于复杂流体的模拟，因为它们导致界面捕获（而不是跟踪）方法，并且界面物理可以直接纳入中尺度水平。为了在仿真能力方面取得重大进展，本提案重点关注三个相关领域。首先，必须制定改进的晶格玻尔兹曼方程（LBE）模型，该模型始终是从动力学理论推导出来的，并且可以显示出再现感兴趣的宏观现象。其次，必须设计有效的数值算法对所建立的LBE模型进行离散和求解。最后，这些方法必须在感兴趣的规范流上进行验证，并在更复杂的工程应用程序上进行演示。虽然LBE方法已经显示出模拟复杂流体现象的潜力，但这些方法很少受到严格的数学分析的影响，而这些分析已经成功地推动了最先进的有效解偏微分方程。因此，本提案的中心目标是通过这些方法的更严格的数学公式，以及通过应用适当的现有数值算法，结合开发新的高效数值技术，提高LBE技术在多相和多组分流体流动模拟中的能力。为此，该提案汇集了在动力学理论、LBE方法、数值分析和流体力学等不同领域具有广泛专业知识的高级人员和外部（未资助）合作者。所提出的工作的智力价值在于，一方面，在动力学理论和达到的宏观极限方面，对晶格玻尔兹曼方法有了更好的理论理解，另一方面，将这些方法解释为通过应用数值分析技术进行研究的离散方程系统。后一个领域的努力代表了一个相对未开发的途径，具有巨大的新进展潜力。根据目前的结果和我们广泛的研究经验，拟议的工作包括一系列高风险任务和目标，这些任务和目标被认为是相对直接的。这项工作所针对的更广泛的影响遵循三个中心主题。首先，这项工作涉及到将晶格玻尔兹曼方法推广到更广泛和更多样化的社区，以刺激跨学科的进步，特别是在数学和计算机科学领域。其次，该提案的合作性质，涉及两个美国机构和几个外部合作者，是开发复杂流体模拟数值方法的强大程序的核心。第三，一个强大的复杂流体模拟项目将有助于研究生的招聘和培训，通过直接资助研究生，以及通过开发项目基础设施来促进向经验不足的学生介绍计算技术。该提案是根据NSF招标NSF-04-538：数学科学：与科学和工程接口的创新而提交的。各自的认知项目官员是t.j. Mountziaris （CTS）和Leland Jameson （MPS）。

Efficient Lattice Boltzmann Methods for Multiphase and Multicomponent FlowsThe overall objective of this proposal is to advance the state-of-the-art in numerical simulations for multi-phase and multi-component flows through the formulation, implementation, and validation of efficient lattice Boltzmann methods designed specifically for such problems. Lattice Boltzmann methods are mesoscopic approaches, based on kinetic theory, which operate at the level of particle distribution functions in phase space. These methods are particularly well suited to the simulation of complex fluids, since they result in interface capturing (as opposed to tracking) methods, and the interface physics may be incorporated directly at the meososcale level.In order to achieve significant progress in simulation capability, the proposal focuses on three related areas. Firstly, improved lattice Boltzmann equation (LBE) models, which are consistently derived from kinetic theory, and can be shown to reproduce the governing macroscopic phenomena of interest, must be formulated. Secondly, efficient numerical algorithms must be devised for discretizing and solving the developed LBE models. Finally, these methods must be validated on canonical flows of interest, and demonstrated on more complex engineering applications as well.While LBE methods have shown potential for simulating complex fluid phenomena, these methods have seldom been subject to the rigorous mathematical analysis that has been so successful at advancing the state-of-the-art in efficient solvers for partial-differential equations. A central objective of this proposal is thus to advance the capability of LBE techniques for multi-phase and multi-component fluid flow simulations through a more rigorous mathematical formulation of these methods, as well as through the application of suitable existing numerical algorithms, combined with the development of novel efficient numerical techniques. To this end, the proposal brings together senior personnel and external (unfunded) collaborators with extensive expertise in the disparate fields of kinetic theory, LBE methods, numerical analysis and fluid mechanics.The intellectual merit of the proposed work rests, on the one hand, in the development of a better theoretical understanding of lattice Boltzmann methods, both in terms of kinetic theory and the achieved macroscopic limits, and on the other hand, in the interpretation of these methods as discrete systems of equations to be investigated through applied numerical analysis techniques. The effort in this latter area represents a relatively unexplored avenue with substantial potential for novel advances. The proposed work includes a portfolio of high-risk tasks and objectives considered to be relatively straightforward, based on current results and our extensive research experience.The broader impacts targeted in this work follow three central themes. First, the work involves the promotion and exposure of lattice Boltzmann methods to a broader and more diverse community, in order to stimulate inter-disciplinary advances, drawing particularly on the fields of mathematics and computer science. Second, the collaborative nature of this proposal, involving two US institutions and several outside collaborators, is central to the development of a strong program in numerical methods for complex fluid simulations. Third, a strong program in the simulation of complex fluids will aid in the recruitment and training of graduate students, through the direct funding of graduate students, as well as through the development of program infrastructure required to facilitate the introduction of computational techniques to less experienced students. This proposal is being submitted in response to NSF solicitation NSF-04-538: Mathematical Sciences: Innovations at the Interface with the Sciences and Engineering. The respective cognizant program officers are T. J. Mountziaris (CTS), and Leland Jameson (MPS).