Kinetic Theory Method for Large Eddy Simulation of Turbulence

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9974289In this work, we plan to explore and apply a fundamentally new approach to large-eddy simulation (LES) of turbulence, viz. the use of a Boltzmann kinetic level representation of the flow. Conventional approaches to LES are based on solving a system of modified Navier-Stokes equations at the continuum level. While such an approach has achieved many interesting results, it also encounters intrinsic difficulties (e.g. in providing faithful turbulent behavior at boundaries). Owing to recent successes with the lattice Boltzmann method, we believe there is significant potential in approaching the problem from a new angle. That is, we propose the use of the Boltzmann equation representation of fluid dynamics. Such a representation is not only suitable for describing particle motions, but may also be a useful way of studying large-scale fluid turbulence properties once some appropriate averaging procedure is constructed. In this work, we plan to carry out an extensive series of theoretical and computational studies of turbulence dynamics by formulating such a Boltzmann description. The specific tasks include model formulation, simulation results, memory and history effects, reformulation of wall models and boundary conditions, and initial applications to multiphase turbulent flows.The work to be done here may have long-lasting impact on our ability to simulate fluid flows in real-world systems. The huge range of eddy sizes in turbulence precludes direct solution of the flow equations at all scales for full-scale systems. The novelty of the lattice Boltzmann method is that it circumvents some of the intrinsic limitations of conventional computers in order to achieve realistic flow simulations. By coupling of this method to advanced ideas on large-eddy simulation, we expect to achieve progress that would not otherwise be possible on these difficult flow problems. In particular, the lattice Boltzmann method for large-eddy simulation allows the efficient formulation of near-wall boundary conditions that have so far escaped analysis. It is also possible that the new formulations to be established here will suggest new computer architectures that will enable full-scale flow simulations.