Entropy-Consistent Moment-Closure Approximations of Kinetic Boltzmann Equations

点击翻译按钮获取中文摘要

This research is concerned with the development of mathematical models and corresponding state-of-the-art computational methods for simulating and predicting the dynamics of complex fluid systems, such as those arising from multiphase flows and plasma. The ability to predict the dynamics of these complex fluid systems is of vital importance in understanding a wide range of phenomena such as particulate flow in the atmosphere, fuel sprays in combustion engines, magnetically-confined fusion reactors, laser-plasma accelerators, space weather, and astrophysical events. The underlying physics of such systems are often well-represented by kinetic models that represent the state of the fluid in terms of probability density functions. The main challenge in accurately simulating these kinetic models is that solutions live in a high-dimensional phase space and contain information over wide-ranging spatial and temporal scales. The goal of this research is to develop reduced models that simultaneously capture the important physics and can be more readily solved on modern computer architectures. As part of this research effort, graduate and undergraduate students will be trained in mathematical modeling and computational mathematics. Students from groups that are underrepresented in applied and computational mathematics will be encouraged to participate in the research efforts. The primary objective of this research is to develop accurate and efficient computational methods for solving kinetic models of both polydisperse multiphase flows and plasma flows via entropy-consistent moment closures. The purpose of moment-closure techniques is to reduce high-dimensional kinetic models to more computationally tractable approximations. However, determining a suitable moment closure is a mathematical challenge; a general approach that combines desirable mathematical features remains elusive. This research will pursue two related approaches: (1) using quasi-exponential representations of the underlying kinetic distribution functions, and (2) using delta functions in conjunction with entropy maximization. Novel moment-inversion algorithms and high-order numerical schemes will be developed. The resulting codes will be implemented on massively parallel computers. These techniques will be applied to problems in polydisperse multiphase flows and plasma flows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.