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

多相和多组分流的高效格子Boltzmann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格子Boltzmann方法的制定、实施和验证，推进多相和多组分流数值模拟的最新技术水平。格子玻尔兹曼方法是基于动力学理论的介观方法，其在相空间中的粒子分布函数水平上操作。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，界面物理学可以直接纳入中尺度水平，为了在模拟能力方面取得重大进展，该提案侧重于三个相关领域。首先，改进的格子玻尔兹曼方程（LBE）模型，这是一贯来自动力学理论，并可以重现感兴趣的宏观现象，必须制定。其次，必须设计有效的数值算法来离散和求解所开发的LBE模型。最后，这些方法必须在典型的感兴趣的流动上进行验证，并在更复杂的工程应用中进行演示。虽然LBE方法在模拟复杂的流体现象方面显示出了潜力，但这些方法很少受到严格的数学分析的影响，而严格的数学分析在推进偏微分方程的有效求解方面取得了如此成功。因此，本建议的一个中心目标是通过这些方法的更严格的数学公式，以及通过应用合适的现有数值算法，结合新的高效数值技术的发展，提高LBE技术用于多相和多组分流体流动模拟的能力。为此，该提案汇集了高级人员和外部人员，（未资助）合作者在动力学理论，LBE方法，数值分析和流体力学的不同领域具有广泛的专业知识。拟议工作的智力价值在于，一方面，在动力学理论和实现的宏观极限方面，对晶格玻尔兹曼方法有了更好的理论理解，另一方面，在解释这些方法作为离散系统的方程进行调查，通过应用数值分析技术。后一个领域的努力代表了一个相对未探索的途径，具有取得新进展的巨大潜力。根据目前的成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简单的。首先，这项工作涉及到推广和暴露晶格玻尔兹曼方法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，这项提案的合作性质，涉及两个美国机构和几个外部合作者，是核心的复杂流体模拟数值方法的强大程序的发展。第三，一个强大的程序在复杂流体的模拟将有助于招聘和培养研究生，通过研究生的直接资助，以及通过所需的程序基础设施的发展，以促进计算技术的介绍经验不足的学生。该提案是为了响应NSF征集NSF-04-538：数学科学：与科学和工程接口的创新。相应的认知程序官员是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).