Efficient particle . methods for solving the Boltzmann equation

A new particle simulation method for solving the Boltzmann equation is presented and tested. This method holds a significant computational efficiency advantage for low-signal flows compared to traditional particle methods such as the Direct Simulation Monte Carlo (DSMC). More specifically, the proposed algorithmn can efficiently simulate arbitrarily small deviations from equilibrium (e.g. low speed flows) at a computational cost that does not scale with the deviation from equilibriumn, while maintaining the basic algorithmic structure of DSIMC. This is achieved by incorporating the variance reduction ideas presented in [L. L. Baker and N. G. Hadjiconstantinou, Physics of Fluids, vol 17, art. no 051703, 2005] within a collision integral formulation; the latter ensures that the deviation fromi equilibrium remains finite and thus the calculation remains stable for collision dominated flows, in contrast to previous attempts. The formulation, developed within this thesis, is described in detail. The resulting scheme is validated for a wide range of Knudsen numbers (ratio of molecular mean free path to characteristic flow lengthscale) ranging from collision-dominated flow to collisionless flowand a wide range of deviations from equilibrium. Excellent agreement is found with DSMC solutions for linear and weakly non-linear flows. Thesis Supervisor: Nicolas G. Hadjiconstantinou Title: Associate Professor of Mechanical Engineering Acknowledgments This research experience has been very enriching from an acadelnmic perspective 1nld also b eneficial to my developmente. I would like to express mny sincere appreciations to mly supervisor, Pr. Nicolas G. Ha(djiconstantinou for welcolming mie in his research team and involving ine in a very exciting project. I also thank hiiim for his advice, guidance and continuous slupport during the carrying-out of this work. His extensive knowledge and creative thinking have been an invaluable help. I am gratful to Lowell L. Baker for his detailed explanations and help with the formulation of the problem. The numerous in-depth discussions with him have been a major source of inspiration. I also thank him for giving ime his DSNIC code. I would like to thank Husain Al-Mohssen for managing the computer cluster. I would not have been able to run my simulations without this indispensable tool. Thanks to umy fellow research students Lowell, Husain, Ghassan and Ho-Man fromi room 3-355A. They contributed to making the office a lively place. Last but not least, I would like to thank miy family for supporting me from France.