Bulletin of the American Physical Society
73rd Annual Gaseous Electronics Virtual Conference
Volume 65, Number 10
Monday–Friday, October 5–9, 2020; Time Zone: Central Daylight Time, USA.
Session MW3: Modeling and Simulation: Computational Methods ILive
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Chair: Satoshi Hamaguchi, Osaka University |
Wednesday, October 7, 2020 8:00AM - 8:30AM Live |
MW3.00001: Machine learning for solving the Boltzmann equation of charged particle swarms Invited Speaker: Satoru kawaguchi Artificial neural network (ANN) is one of the models used in the machine learning and has high ability for approximating a function. Recently, a novel numerical method for solving partial differential equations (PDEs) where the latent solution of PDE is approximated by ANN was proposed, and the method is called physics informed deep learning [1]. This method does not require the discretization of PDE and is therefore able to deal with complex geometry and high-dimensional PDEs easily. The Boltzmann equation is one of the most important PDEs in our community since this equation governs the velocity distribution function of charged particles, which specifies those transport coefficients and rate coefficients for reactions induced by charged particle collisions. We have developed a novel direct numerical solution method of the Boltzmann equation for electron swarms by applying the physics informed deep learning [2]. Our method does not require the expansion of the electron velocity distribution function (EVDF) by the orthogonal functions, such as Legendre polynomials. As a benchmark, the EVDF in Ar gas under a DC uniform electric field was calculated by our method and was found to agree with the EVDF calculated by the Monte Carlo method. Recent progress of our method will be also presented. [1] M Raissi, P Perdikaris, and G E Karniadakis, J. Compt. Phys. 378, 686 (2019) [2] S Kawaguchi, K Takahashi, H Ohkama and K Satoh, Plasma Sources Sci. Technol. 29, 025021 (2019) [Preview Abstract] |
Wednesday, October 7, 2020 8:30AM - 8:45AM Live |
MW3.00002: A machine learning approach to the solution of Poisson's equations for plasma simulations Jan Trieschmann, Tobias Gergs, Yue Liu, Thomas Mussenbrock The solution of Poisson's equation in one or multiple dimensions is an essential requirement in many plasma simulations. While the computational effort is minor in 1D configurations, it may become significant in multi-dimensional simulation setups. We propose a potential remedy using a machine learning Poisson solver. The approach utilizes an unsupervised learning scheme to train an artificial neural network on charge density distributions from Particle-in-Cell plasma simulations. A proof of concept for the inference of the artificial neural network on the electric potential for a given space charge density is demonstrated and discussed. Moreover, the unsupervised learning procedure, the incorporation of boundary conditions, an accuracy assessment, and implementation aspects within Particle-in-Cell simulations are detailed. It is concluded that the proposed solution scheme is applicable in other simulation methods (e.g., plasma fluid simulations) as well. [Preview Abstract] |
Wednesday, October 7, 2020 8:45AM - 9:00AM Live |
MW3.00003: Deep learning for thermal plasma modelling Linlin Zhong Numerical modelling is an essential approach to understanding the behavior of thermal plasmas in various industrial applications. We propose a deep learning method for solving the partial differential equations in thermal plasma models. In this method a deep feed-forward neural network is constructed to surrogate the solution of the model. A loss function is designed to measure the discrepancy between the neural network and the equations describing thermal plasmas. A good neural network is obtained by minimizing this loss function. We demonstrate the power of this deep learning method by solving a 1-D arc decaying model which is consist of three cases: stationary arc, transient arc without considering radial velocity, and transient arc with radial velocity respectively. The results show that the deep neural networks have excellent ability to express the differential equations describing thermal plasmas. This could bring us a new and prospective numerical tool for thermal plasma modelling. [Preview Abstract] |
Wednesday, October 7, 2020 9:00AM - 9:15AM Live |
MW3.00004: Fast and accurate simulations of electrons in CO2 using Monte Carlo Flux Luca Vialetto, Pedro Viegas, Savino Longo, Paola Diomede Numerical models are fundamental to understand mechanisms underlying plasma-assisted activation of CO$_2$. Due to the complex chemical network and the presence of multiple time scales, those models require fast and accurate computational approaches. In this work, approximations that are usually employed in the study of electron kinetics in CO$_2$ are analyzed, together with strategies to overcome them. A fully native Monte Carlo Flux (MCF) code has been developed to calculate steady-state and time-dependent electron velocity distribution functions (EVDF). The MCF method is based on an highly efficient variance reduction technique and it has been extended to take into account the thermal velocity distribution function of the gas molecules and an accurate description of rotationally and vibrationally excited states.Deviations of rate coefficients up to 70$\%$ between MCF and two-term Boltzmann solvers are found, due to the anisotropy of the EVDF. Moreover, this extension provides a better agreement with measured transport coefficients at low reduced electric fields ($E/N$). A good agreement between experimental values of dissociation rate coefficients and MCF calculations is found at moderate $E/N$ values after careful consideration and analysis of several cross sections data set. [Preview Abstract] |
Wednesday, October 7, 2020 9:15AM - 9:45AM Live |
MW3.00005: Low Temperature Kinetic Plasma Simulations for New and Future Supercomputer Architectures Invited Speaker: Andrew Powis Kinetic simulations for low-temperature plasmas are widely applicable to many modern plasma applications, including materials processing and etching, plasma switches, and spacecraft electric propulsion. At the Princeton Plasma Physics Laboratory we are developing simulation tools to enable engineering prototyping of low-temperature plasma devices. One of our tools, based on the standard particle-in-cell method, has been written from the ground up to take advantage of modern supercomputing architectures. This includes targeting the multi-level parallelism inherent to new chips, as well as heterogeneous architectures such as CPU-GPU systems. Specific challenges inherent to low-temperature plasma kinetic codes include the increasing importance of Monte-Carlo collision algorithms, as well as the challenges associated with solving the elliptical Poisson equation on very large simulation grids. Here we explore these challenges, and offer some ideas on how they can be handled on modern supercomputers, particularly those with CPU-GPU architecture. We also present profiling results which demonstrate the advantages of writing algorithms which can specifically target these new and future supercomputers. [Preview Abstract] |
Wednesday, October 7, 2020 9:45AM - 10:00AM |
MW3.00006: Multi-scale two-domain numerical modeling of stationary positive DC corona discharge/drift-region coupling Nicolas Monrolin, Franck Plouraboué We asymptotically derive a multi-scale/two-domain approach for corona discharge numerical modeling. We show how the initial non-linear, elliptic-hyperbolic non-local problem can be formulated into two coupled ones from a multipole expansion of the radiative photo-ionization source term resulting in truncating it to a local integral in corona discharge domain. The proposed approach is both monolithic and two-domain, producing two asymptotic regions, an inner-one associated with corona discharge, and an outer-one, the drift region. We provide the coupled conditions between the two domains, as well as thoughtfully analyze the electron flux feeding of the inner corona discharge created from photo-ionization in the drift region. This coupling is taken care of by Lagrange multipliers, within a variational formulation, leading to a hierarchy of non-linear coupled problems. Numerical convergence and validations of the finite element implementation of the approach are provided. Comparison with various experimental results convincingly demonstrate the applicability of the method, which avoid tuning parameters dedicated to each specific configuration, but, on the contrary, exclusively and robustly relies on known and measurable physical quantities. [Preview Abstract] |
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