Collaborative proposal: Higher-Order Two-Fluid Methods for Simulations of Particle-Laden Flow

在这项工作中，pi和他们的学生基于一组新的耦合双流体双曲守恒偏微分方程和混合weno -谱方法开发了一种高阶双流体方法。双流体模型是前所未有的，从第一原理获得，利用欧拉方法来描述粒子，这主要是通过粒子的拉格朗日框架中的低阶方法来建模的。在欧拉坐标系中，粒子相位是通过一组控制粒子性质的概率密度函数行为的双曲欧拉输运方程来建模的。采用一种新的基于矩量法的统计方法，通过平均Liouville方程推导出了这些方程。研究人员提出了一种基于高阶分辨率、混合多域weno -谱方法的双流体模型方法。预计高分辨率方法将改进现有的低阶方法，可以清晰地捕捉不连续界面和激波，同时准确地分辨小尺度、非定常颗粒负载的流动特征。本建议的重点是发展一个稳定和一致的捕获不连续的粒子-气体界面，以及一个稳定和一致的源耦合粒子和气相。另一个重点将放在耦合气体和粒子偏微分方程的非线性、奇异和刚性源项的正则化上。双流体方法将根据已发布的基准进行评估，包括单向耦合各向同性湍流和双向耦合激波粒子相互作用，用更成熟的欧拉-拉格朗日方法计算。爆炸和燃烧过程产生了流体湍流和冲击与粒子密切相互作用的环境。各种工程系统和自然过程涉及高速粒子动力学、激波-湍流相互作用和粒子流相互作用；这种现象在爆炸引起的泥石流和污染物扩散、控制超音速燃烧、高性能航空航天和电子元件的高速涂层过程中起着关键作用。例如，冰岛的火山爆发产生了冲击，加速了湍流气流和微型粉尘颗粒，这些颗粒在几天内被携带了数百英里，不仅污染了环境，而且在很长一段时间内影响了空中交通。提出的研究开发了一种先进的数值工具，能够（改进）计算这些流动，最终将增强对一大类工程和环境问题的理解。这些知识可以直接用于设计改进、污染控制和爆炸过程对社会的影响。此外，该提案通过让学生参与SDSU的数学、工程、科学成就（MESA）项目，增加了STEM教育中代表性不足群体的学生数量。

In this effort the PIs and their student develop a high-order two-fluid method based on a new set of coupled two-fluid hyperbolic conservation PDEs and a Hybrid WENO-spectral method. The two-fluid model is unprecedented, obtained from first principles utilizing an Eulerian approach for the description of particles, which have been predominantly modeled through lower-order methods in the Lagrangian frame of the particle. In the Eulerian frame, the particle phase is modeled through a set of hyperbolic Eulerian transport equations governing the behavior of the Probability Density Function of particle properties. The equations are derived by a novel statistical method based on a method of moments via an averaged Liouville equation. The PIs propose to develop a method based on a high-order resolution, hybrid multidomain WENO-spectral method for the two-fluid model. The high- resolution method is projected to improve over existing lower- order method by capturing discontinuous interfaces and shocks sharply, while accurately resolving small scale, unsteady particle-laden flow features. The focus of this proposal is on the development of a stable and consistent capturing of discontinuous particle-gas interfaces as well as a stable and consistent source coupling between the particle and gas phases. Another focus will be on the regularization of non- linear, singular and stiff source terms that couple the gas and particle PDEs. The two-fluid method will be assessed against published benchmarks, including a one-way coupled isotropic turbulence and two-way coupled shock particle interaction, computed with a more established Eulerian- Lagrangian method.Explosions and combustion processes generate environments where fluid turbulence and shocks have an intimate and mutual interaction with particles. Various engineered systems and natural processes involve high speed particle dynamics, shock- turbulence interaction, and particle flow interactions; such phenomena play key roles in debris flow and contaminant spread due to explosions, controlling supersonic combustion, high- speed coating processes for high-performance aerospace and electronic components. The volcanic explosions in Iceland, for example, generated shocks, accelerated turbulent gas flows and micro-scale dust particles that were carried for hundreds of miles over several days not only polluting the environment but affecting air traffic for an extended period of time. The proposed research develops an advanced numerical tool that enables (improved) computation of these flows which will ultimately enhance understanding of a large class of engineering and environmental problems. This knowledge can be used directly in design improvements, control of pollution and the effects of explosion processes on society. This proposal, moreover, increases the number of students from underrepresented groups in STEM education by involving students in the Mathematics, Engineering, Science Achievement (MESA) program at SDSU.