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最悬而未决的问题之一。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一个例子。微型PPT中的流动是部分电离的碰撞等离子体，呈现出从连续介质到稀薄(或非平衡)区域的转变。为了成功地模拟这种多尺度流动，提出了一种新的随机混合算法，该算法将适用于高度非平衡流态的直接模拟蒙特卡罗方法和适用于其他区域的连续介质方法相结合，以提高计算效率。利用新算法，研究将集中于微推力器内部流动的数值模拟。最后，通过随机模拟对推力器的比冲、推力等性能进行了优化。提出的活动的智力优势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，该研究的意义之一是在动力学方法和连续介质方法之间建立了一个随机接口，以交换统计分布而不是时空平均。将所提出的工具应用于微推进器的研究，以期通过优化其几何形状来提高其性能。这项拟议的工作将广泛地扩展对当前感兴趣的许多应用中的多尺度流动行为的理解。它将有助于开发效率更高的新型微推进装置，这对下一代微航天器非常重要。此外，将开发的方法可应用于工程、物理和生物学中的许多应用，包括但不限于高超声速返回飞行器、聚变毯子的热流体和超声波溶解血块。拟议的工作将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培训来继续和扩大皮？S教育外联活动。计划进行本科生和研究生的跨学科培训。

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.