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

在这项工作中，PI和他们的学生开发了一个高阶双流体方法的基础上，一套新的耦合双流体双曲守恒偏微分方程和混合WENO谱方法。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，这主要是通过较低阶的方法在拉格朗日框架中的粒子建模。在欧拉框架中，粒子相通过一组双曲欧拉输运方程来建模，该方程控制粒子属性的概率密度函数的行为。该方程是由一种新的统计方法的基础上，通过平均刘维尔方程的矩量法。PI建议开发一种基于高阶分辨率，混合多域WENO谱方法的双流体模型的方法。高分辨率的方法，预计将改善现有的低阶方法捕捉不连续的界面和冲击急剧，同时准确地解决小尺度，非定常颗粒负载流的功能。 该提案的重点是发展一个稳定和一致的捕获不连续的颗粒-气体界面，以及稳定和一致的源耦合之间的颗粒和气相。另一个重点将是非线性，奇异和刚性源项耦合气体和粒子偏微分方程的正则化。双流体方法将根据已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，用更成熟的欧拉-拉格朗日方法计算。爆炸和燃烧过程产生的环境中，流体湍流和激波与粒子有密切的相互作用。各种工程系统和自然过程涉及高速粒子动力学、冲击-湍流相互作用和粒子流相互作用;这些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部件的高速涂层过程中起关键作用。例如，冰岛的火山爆发产生了冲击，加速了湍流气流，并在几天内将微型尘埃颗粒带到数百英里之外，不仅污染了环境，而且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，使（改进）这些流量的计算，这将最终提高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、污染控制以及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（梅萨）计划，增加了STEM教育中代表性不足群体的学生人数。

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.