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，用于模拟湍流液滴负载流植根于粒子传输的概率为基础的描述。这需要确定空间和时间中的粒子密度函数的演变，再加上载体相（气体或液体）的湍流。该函数的知识使得能够在载气流的控制方程中与通过质量、动量和能量源的流一致地耦合。过去阻止这种方法取得进展的主要数学困难是分布函数的独立变量空间的高维性，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多个额外维度。该提案的变革性在于：（i）设计一种方法，用于整合传输方程的分布函数，该分布函数在计算上是可行的，（ii）在一个有效的预测和模块化工具中实施数值方法，以及（iii）扩展大气云模拟中载气与微物理相互作用的目前无法访问的方面的知识。 此外，与马克斯-普朗克气象研究所的一个小组合作，将确保有效转让和传播拟用于物理气象学领域的技术。多相流的预测，特别是分散在主气体中的固体或液体颗粒，是具有挑战性的和计算繁重。这些流动出现在自然现象中;包括云动力学，沙尘暴和草原火灾;以及食品和化学加工以及化学合成和推进等工业应用。高度湍流的流动与大量不同形状和大小的颗粒（数百万到数十亿甚至更多）之间的相互作用，以不同的速度向不同的方向移动，经历相变和/或化学反应，导致复杂的数学问题。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获得的分散颗粒流。这项研究将使高保真度的计算，包括在小规模和大规模的现象一致。加强对这些流动的预测具有许多科学和社会效益;例如，因为大气流动对于改善天气预报和更好地了解我们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.