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

在这项工作中，PI和他们的学生发展了一种基于一组新的耦合双流体双曲守恒偏微分方程组和混合WENO谱方法的高阶双流体方法。双流体模型是史无前例的，它是从利用欧拉方法描述粒子的第一原理获得的，粒子主要是通过粒子的拉格朗日框架中的低阶方法建模的。在欧拉标架中，粒子相通过一组双曲型欧拉输运方程来模拟，该方程控制粒子性质的概率密度函数的行为。用一种新的基于矩方法的统计方法，通过一个平均的Liouville方程推导出了这些方程。PI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。高分辨率方法预计将通过捕捉不连续界面和激波来改进现有的低阶方法，同时精确地解决小尺度、非定常颗粒携带的流动特征。这一提议的重点是发展对不连续颗粒-气体界面的稳定和一致的捕获，以及颗粒和气相之间稳定和一致的源耦合。另一个焦点将是耦合气体和粒子PDE的非线性、奇异和刚性源项的正则化。双流体方法将根据公布的基准进行评估，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，使用更成熟的欧拉-拉格朗日方法计算。爆炸和燃烧过程产生流体湍流和激波与粒子密切和相互作用的环境。各种工程系统和自然过程涉及高速粒子动力学、激波-湍流相互作用和颗粒流相互作用；这些现象在泥石流和爆炸引起的污染物扩散、控制超音速燃烧、高性能航空航天和电子元器件的高速涂层过程中发挥着关键作用。例如，冰岛的火山爆发产生了冲击波，加速了湍流，并在几天内携带了数百英里的微小尘埃颗粒，不仅污染了环境，还在很长一段时间内影响了空中交通。拟议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，这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，这项提议通过让学生参加SDSU的数学、工程、科学成就(MESA)计划，增加了STEM教育中来自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.