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

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设备或低气体密度下，如在高海拔大气现象和需要真空条件的制造过程中。将开发验证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，并为持续发展提供用户和贡献者基础。具体来说，演示案例将包括几个经典的稀薄流动问题，如傅里叶和库埃特流动、正常激波、压力驱动和热驱动的通道流动以及气体混合物中的热扩散。计算求解器将弥合现有连续体和原子模拟之间的差距，使科学家和工程师能够解决迄今为止难以解决的低速气体混合流动的非平衡输运问题，这些问题具有基础和实际意义。该项目将解决的具体应用包括微量气体分离和气体分析技术，以及高性能集成电路的超高热流密度蒸发冷却。计算求解器将发布给研究界，其结果将整合到课程中，以教育学生。新的计算框架是基于不连续伽辽金快速谱（DGFS）方法的，该方法允许对任意几何形状和气体混合物的完整玻尔兹曼方程进行精确的确定性求解。积分-微分玻尔兹曼方程的确定性解在物理和速度空间和时间上具有高阶精度，没有统计噪声和采样误差，特别适用于非定常和低速流动的模拟。由于玻尔兹曼方程的物理相空间和速度相空间的多维性，稀薄流动的确定性解的计算要求很高；因此，它需要在大规模并行架构上高效的求解器。玻尔兹曼方程的高阶h/p方法表现出良好的并行标度，并作为提出的DEEKSHA框架的基础。为了扩大项目的影响，计算解算器将在通用的公共许可下发布。向最终用户社区传播的计划活动包括：a)开发人员讲习班和会议模拟训练营；b)将研究成果整合到普渡航空航天学院和数学系的课程中，并在Nanohub上举办网络研讨会和互动工具；c)通过普渡大学工程学院暑期本科生研究员项目为本科生提供研究经验。该奖项反映了美国国家科学基金会的法定使命，并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。

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.