The 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).
