A Novel Probabilistic-Based Approach to the Simulation of Disperse Two-Phase Flows with Application to Atmospheric Science

研究人员将开发和研究一种新的计算方法，用于模拟基于粒子输运的概率描述的湍流液滴流动。这需要确定颗粒密度函数在空间和时间上的演变，以及载体相(气体或液体)的湍流。对该函数的了解使得能够在载气流动的控制方程中与流经质量、动量和能量源的流动保持一致的耦合。过去阻碍这种方法取得进展的主要数学困难是分布函数的自变量空间的高维，这使得传统的计算技术对于当前或可预见的计算资源来说是无效的。这项研究的主要思想是使用一种新的非线性全局基函数投影方法，该方法浓缩了问题的几个额外维度。这项提议的变革性在于：(1)设计了一种方法，用于计算服从计算的分布函数的输运方程，(2)以有效的预测和模块化工具实施数值方法，以及(3)扩展大气云模拟中与载气相互作用的微物理方面目前无法理解的方面的知识。此外，与马克斯·普朗克气象研究所的一个小组合作，将确保将拟议的技术有效地转移和传播到物理气象学领域。多相流动的预测，特别是分散在主体气体中的固体或液体颗粒，具有挑战性和计算上的繁琐。这些流动产生于自然现象；包括云动态、沙尘暴和草原火灾；以及工业应用，如食品和化学加工以及化学合成和推进。高度湍动的流动与极大量不同形状和大小、以不同速度沿不同方向移动的粒子(数百万到数十亿甚至更多)之间的相互作用，经历了相变和/或化学反应，导致了一个复杂的数学问题。拟议的研究将对理解广泛的科学和工程现象产生重大影响，这些现象涉及目前无法接触到的具有分散颗粒的流动。这项研究将使高保真计算能够始终如一地纳入小尺度和大尺度的现象。加强对这些流动的预测有许多科学和社会效益；例如，因为大气流动对于改进天气预报和更好地了解我们这个星球的全球能源平衡至关重要。

The investigator will develop and study a new computational approach for the simulation of turbulent droplet-laden flows rooted in the probabilistic-based description of particle transport. This requires the determination of the evolution of the particle-density function in space and time, coupled with the turbulent flow of the carrier phase (gas or liquid). Knowledge of this function enables consistent coupling with the flow through mass, momentum, and energy sources in the governing equations of the carrier gas flow. The main mathematical difficulty that has prevented this approach from progressing in the past is the high dimensionality of the space of independent variables of the distribution function, which renders traditional computational techniques ineffective with current or foreseeable computational resources. The main idea of the research is the use of a new non-linear global basis function projection approach that condenses several of the extra dimensions of the problem. The transformative nature of the proposal is in (i) devising a methodology for integrating the transport equation for the distribution function that is computationally amenable, (ii) implementing the numerical methodology in an efficient predictive and modular tool, and (iii) extending the knowledge of the currently inaccessible aspects of the microphysics interaction with the carrier gas in atmospheric cloud simulations. Furthermore, collaboration with a team at Max-Planck Institute for Meteorology will ensure the effective transfer and dissemination of the technology that is proposed to the area of physical meteorology. The prediction of multi-phase flows, particularly solid or liquid particles dispersed in a host-gas, is challenging and computationally onerous. These flows arise in natural phenomena; encompassing cloud dynamics, dust storms and grassland fires; and industrial applications such as food and chemical processing as well as chemical synthesis and propulsion. The interactions between a highly turbulent flow and the extremely large number of particles (millions-to-billions and beyond) of different shape and size, moving in different directions with different velocities, that undergo phase transformation and/or chemical reactions, lead to a complex mathematical problem. The proposed research will make a significant impact in the understanding of a wide range of science and engineering phenomena involving flows with dispersed particles that are currently inaccessible. The research will enable high-fidelity computations that incorporate phenomena at the small and large scales consistently. Enhancement in the prediction of these flows has numerous scientific and societal benefits; e.g., because atmospheric flows are critical to improve weather prediction and to better understand the global energy balance of our planet.