CDS&E: DEterministic Evaluation of Kinetic Boltzmann equation with Spectral H/p/v Accuracy (DEEKSHA)

CDS

• 批准号: 1854829
• 负责人: Alina Alexeenko
• 金额: $ 33.12万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1854829&HistoricalAwards=false
• 关键词: CDS& DEterministic; Evaluation; Kinetic; Boltzmann

The goal of this project is to develop an open-source massively parallel computational software DEEKSHA (DEterministic Evaluation of Kinetic Boltzmann equation with Spectral h/p/v adaptivity and Accuracy) for scientific simulation of rarefied gas flows. Such gas flows occur in microdevices or at low gas densities, as in high-altitude atmospheric phenomena and in manufacturing processes that require vacuum conditions. Verification benchmarks and end-user demos will be developed to facilitate adoption of the new scientific simulation software by academia and industry and to provide the user and contributor base for sustained development. Specifically, the demonstration cases will include several classical rarefied flow problems such as Fourier and Couette flows, normal shock wave, pressure-driven and thermally-driven channel flows and thermal diffusion in gas mixtures. The computational solver will bridge the gap between existing continuum and atomistic simulations and would enable scientists and engineers to address so far intractable non-equilibrium transport problems for low-speed gas mixture flows of fundamental and practical interest. The specific applications that will be addressed in this project include trace gas separation and gas analytical technologies as well as ultra-high-heat flux evaporation cooling for high-performance integrated circuits. The computation solver will be released to the research community, and the results will be integrated into courses to educate students.The new computational framework is based on the Discontinuous Galerkin Fast Spectral (DGFS) method which allows accurate deterministic solution of the full Boltzmann equation for arbitrary geometries and gas mixtures. The deterministic solution of the integro-differential Boltzmann equation is high order accurate in both physical and velocity space and time, free from statistical noise and sampling errors, and is particularly suitable for unsteady and low speed flow simulations. Due to the multi-dimensionality of physical and velocity phase space of the Boltzmann equation, the deterministic solution of rarefied flows is computationally demanding; hence, it requires solvers that are efficient on massively parallel architectures. The high-order h/p methods for the Boltzmann equation exhibit excellent parallel-scaling and serve as the basis of the proposed DEEKSHA framework. To broaden the impact of project, the computational solver will be released under a general, public license. The planned activities for dissemination to end-user communities include: a) workshops for developers and simulation bootcamps at conferences; b) integration of research results into courses taught at Purdue School of Astronautics and Aeronautics and Department of Mathematics as well as a webinar and interactive tool on Nanohub; and c) research experiences for undergraduate students through Purdue Engineering Summer Undergraduate Research Fellow program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目的目标是开发一个开源的大规模并行计算软件DEEKSHA（具有光谱h/p/v自适应性和准确性的动力学玻尔兹曼方程的确定性评估），用于稀薄气体流动的科学模拟。这种气体流动发生在微型器件中或低气体密度下，如在高海拔大气现象和需要真空条件的制造工艺中。将制定核查基准和最终用户演示，以促进学术界和工业界采用新的科学模拟软件，并为持续开发提供用户和捐助者基础。具体而言，演示案例将包括几个经典的稀薄流动问题，如傅立叶和Couette流，正激波，压力驱动和热驱动的通道流动和气体混合物中的热扩散。计算求解器将弥合现有的连续介质和原子模拟之间的差距，并将使科学家和工程师，以解决迄今棘手的非平衡输运问题的低速气体混合物流的基本和实际利益。该项目将涉及的具体应用包括痕量气体分离和气体分析技术，以及用于高性能集成电路的超高热通量蒸发冷却。计算求解器将发布给研究界，其结果将被整合到课程中，以教育学生。新的计算框架是基于不连续Galerkin快速谱（DGFS）方法，该方法可以精确确定性解决任意几何形状和气体混合物的完整Boltzmann方程。积分微分Boltzmann方程的确定性解在物理和速度空间和时间上都是高阶精度的，不受统计噪声和采样误差的影响，并且特别适合于非定常和低速流动模拟。由于玻尔兹曼方程的物理和速度相空间的多维性，稀薄流的确定性解在计算上要求很高;因此，它需要在大规模并行架构上高效的求解器。Boltzmann方程的高阶h/p方法具有很好的并行缩放性，并作为建议的DEEKSHA框架的基础。为了扩大项目的影响，计算求解器将在通用公共许可证下发布。计划向最终用户社区传播的活动包括：（a）在会议上为开发人员举办讲习班和模拟训练营;（B）将研究成果纳入普渡大学航天航空学院和数学系教授的课程，以及关于Nanohub的网络研讨会和互动工具;以及c）通过普渡大学工程暑期本科生研究员计划为本科生提供研究经验。该奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equation

• DOI: 10.1016/j.cma.2019.04.015
• 发表时间: 2019-03
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: S. Jaiswal;Alina A. Alexeenko;Jingwei Hu

A Discontinuous Galerkin Fast Spectral Method for Multi-Species Full Boltzmann on Streaming Multi-Processors

流式多处理器上多物种全玻尔兹曼的不连续伽辽金快速谱方法

• DOI: 10.1145/3324989.3325714
• 发表时间: 2019
• 期刊: PASC '19: Proceedings of the Platform for Advanced Scientific Computing Conference
• 作者: Jaiswal, Shashank;Hu, Jingwei;Brillon, Julien K.;Alexeenko, Alina A.
• 通讯作者: Alexeenko, Alina A.

An Adaptive Dynamical Low Rank Method for the Nonlinear Boltzmann Equation

非线性Boltzmann方程的自适应动态低阶方法

• DOI: 10.1007/s10915-022-01934-4
• 发表时间: 2022
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Hu, Jingwei;Wang, Yubo
• 通讯作者: Wang, Yubo

Fast deterministic solution of the full Boltzmann equation on graphics processing units

图形处理单元上完整玻尔兹曼方程的快速确定性解

• DOI: 10.1063/1.5119541
• 发表时间: 2019
• 期刊: AIP Conference Proceedings
• 作者: Jaiswal, Shashank;Hu, Jingwei;Alexeenko, Alina A.
• 通讯作者: Alexeenko, Alina A.

Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts

• DOI: 10.1063/1.5108665
• 发表时间: 2019-05
• 期刊: Physics of Fluids
• 影响因子: 4.6
• 作者: S. Jaiswal;Aaron Pikus;A. Strongrich;I. Sebastião;Jingwei Hu;Alina A. Alexeenko