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概率的湍流液滴流动。这需要确定粒子密度函数在空间和时间上的演化，再加上载体相（气体或液体）的湍流。了解这个函数可以使载气流动的控制方程中通过质量、动量和能量源的流动保持一致的耦合。过去阻碍这种方法发展的主要数学困难是分布函数的自变量空间的高维性，这使得传统的计算技术在当前或可预见的计算资源下无效。该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。该提案的变革性质在于：(i)设计一种方法来积分分布函数的输运方程，该方法在计算上是可接受的，（ii）在有效的预测和模块化工具中实施数值方法，以及（iii）扩展目前难以理解的微物理与大气云模拟中载气相互作用方面的知识。此外，与马克斯-普朗克气象研究所的一个小组合作将确保向物理气象学领域提出的技术的有效转让和传播。多相流的预测，特别是在主气中分散的固体或液体颗粒的预测是具有挑战性的，并且计算量很大。这些流动是自然现象；包括云动力学、沙尘暴和草原火灾；工业应用，如食品和化学加工，以及化学合成和推进。高度湍流与大量不同形状和大小、以不同速度向不同方向移动、经历相变和/或化学反应的粒子（数百万到数十亿甚至更多）之间的相互作用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进入的分散颗粒流动。这项研究将使高保真计算能够一致地结合小尺度和大尺度的现象。加强对这些流量的预测具有许多科学和社会效益；例如，因为大气流动对改善天气预报和更好地了解我们星球的全球能量平衡至关重要。

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.