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

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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.