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

多相流和多组分流动的高效格子Boltzmann方法这项建议的总体目标是通过制定、实施和验证专门为此类问题设计的高效格子Boltzmann方法，促进多相和多组分流数值模拟的最新发展。格子Boltzmann方法是一种基于动力学理论的介观方法，它在相空间中的粒子分布函数水平上工作。这些方法特别适合于复杂流体的模拟，因为它们产生了界面捕捉(而不是跟踪)方法，并且界面物理可以直接结合到微尺度水平上。为了在模拟能力方面取得重大进展，该提案集中在三个相关领域。首先，必须建立改进的格子Boltzmann方程(LBE)模型，该模型始终如一地源自动力学理论，并且可以被证明重现感兴趣的主导宏观现象。其次，必须设计有效的数值算法来离散和求解已开发的LBE模型。最后，这些方法必须在感兴趣的典型流上进行验证，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，而严格的数学分析在推动偏微分方程组的高效求解器方面取得了如此成功。因此，这项建议的一个中心目标是通过更严格的数学表述，以及通过应用合适的现有数值算法，并结合新的高效数值技术的开发，来提高LBE技术用于多相和多组分流体流动模拟的能力。为此，该建议汇集了高级人员和在动力学理论、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外部(无资助)合作者。拟议工作的智力优势在于，一方面在运动学理论和所达到的宏观极限方面对格子Boltzmann方法有了更好的理论理解，另一方面，将这些方法解释为将通过应用数值分析技术研究的离散方程系统。后一领域的努力代表着一条相对未被探索的道路，具有取得新进展的巨大潜力。拟议的工作包括一系列高风险的任务和目标，根据目前的结果和我们广泛的研究经验，被认为是相对简单的。这项工作针对的更广泛的影响遵循三个中心主题。首先，这项工作涉及向更广泛和更多样化的社区推广和展示格子玻尔兹曼方法，以促进跨学科的进步，特别是利用数学和计算机科学领域的知识。其次，这项提议的合作性质，涉及两个美国机构和几个外部合作者，对于开发用于复杂流体模拟的强大的数值方法程序至关重要。第三，一个强大的复杂流体模拟计划将通过对研究生的直接资助以及通过开发所需的计划基础设施来帮助招聘和培训研究生，以促进向经验较少的学生介绍计算技术。这项提案是为了响应NSF-04-538：数学科学：科学与工程交界处的创新而提交的。各自的认知项目官员是T·J·蒙齐亚里(CTS)和利兰·詹姆森(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).