High Order Model, Computation, and Stochastic Hybrid Coupling Continuum-Particle Algorithm with Application to Micro-propulsion

微域多尺度流动模拟是当今计算数学中最困难和尚未解决的问题之一。模拟微脉冲等离子体推力器（PPT）等离子体流产生的微推进就是其中一个例子。微PPT中的流动是部分电离的碰撞等离子体，表现出从连续到稀薄（或非平衡）状态的转变。为了成功地模拟这样的多尺度流动，一种新的随机混合算法相结合的直接模拟蒙特卡罗（DSMC）方法适用于高度非平衡流态和连续的方法在其余的域的效率。利用新算法，研究将集中在数值模拟的微型推力器的内部流动。最后，随机模拟计划，以优化性能特性的推进器，如比冲和推力。拟议活动的智力价值在于开发和分析新的数值算法，并将这些算法应用于多尺度流动问题的大规模模拟。此外，所提出的研究的一个意义是建立一个随机接口之间的动力学和连续的方法来交换的统计分布，而不是时空平均值。提出的工具将被应用于研究微推力器，以改善其性能，通过优化其几何形状。 拟议的工作将广泛地扩展在当前感兴趣的许多应用中的多尺度流的行为的理解。它将协助开发效率更高的新型微型推进装置，这对下一代微型航天器非常重要。此外，待开发的方法可应用于工程、物理和生物学中的许多应用，包括但不限于高超音速重返大气层飞行器、聚变包层的热流体和通过超声波溶解血凝块。建议的工作将继续和扩大PI？通过在圣母大学和太平洋西北国家实验室之间建立强有力的合作，并为学生提供跨学科的培训，来开展教育推广活动。计划对本科生和研究生进行跨学科培训。

Micro-domain multi-scale flow simulation is one of the most difficult and unresolved problems in today's computational mathematics. Simulating micro-propulsion generated by the plasma flow from the micro-pulsed plasma thruster (PPT) is one of the examples. Flow in a micro-PPT is partially ionized collisional plasma exhibiting transition from continuum to rarefied (or non-equilibrium) regime. To successfully simulate such multi-scale flow, a novel stochastic hybrid algorithm combining direct simulation Monte Carlo (DSMC) method suitable for highly non-equilibrium flow regime and continuum methods in the rest of the domain for efficiency is proposed. Using the new algorithm, the study will focus on numerical modeling the internal flow of the micro-thruster. To the end, stochastic simulations are planned to optimize performance characteristics of the thruster such as specific impulse and thrust. The intellectual merit of the proposed activity lies in the development and analysis of new numerical algorithms and application of these algorithms for large scale simulations of multi-scale flow problems. Moreover, one significance of the proposed research is to build a stochastic interface between kinetic and continuum methods to exchange the statistical distribution instead of the spatial-temporal average. Proposed tools will be applied to study the micro-thruster to order to improve their performance by optimizing their geometry. The proposed work will broadly extend the understanding of the behavior of multi-scale flows in many applications of current interest. It will assist in developing new micro-propulsion devices with improved efficiency, which is important for next generation micro-spacecrafts. Moreover, the methods to be developed can be applied to numerous applications in engineering, physics and biology including, but not limited to, hypersonic re-entry vehicles, thermo-fluids of fusion blankets and dissolution of a blood clot by ultrasound. Proposed work will continue and expand the PI?s educational outreach activities by building a strong collaboration between University of Notre Dame and Pacific Northwest National Laboratory and providing interdisciplinary training for students. An interdisciplinary training of undergraduate and graduate student training is planned.