Multidisciplinary benchmarks of a conservative spectral solver for the nonlinear Boltzmann equation

Wilkie, George J.; Keßler, Torsten; Rjasanow, Sergej

doi:10.1016/j.cpc.2023.108812

Multidisciplinary benchmarks of a conservative spectral solver for the nonlinear Boltzmann equation

Journal Article · Mon Jun 26 00:00:00 EDT 2023 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2023.108812· OSTI ID:1995157

^[1]; Keßler, Torsten ^[2]; Rjasanow, Sergej ^[3]

Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
Saarland University (Germany); Eindhoven Univ. of Technology (Netherlands)
Saarland University (Germany)

The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and plasma physics. While these approximations are appropriate in their respective domains, they can be violated in niche but diverse applications which require direct numerical solution of the original nonlinear Boltzmann equation. An expanded implementation of the Galerkin–Petrov conservative spectral algorithm is employed to study a wide variety of physical problems. Enabled by distributed precomputation, solutions of the spatially homogeneous Boltzmann equation can be achieved in seconds on modern personal hardware, while spatially-inhomogeneous problems are solvable in minutes. Here, several benchmarks are presented focusing on accuracy compared to both analytic theoretical predictions and other Boltzmann solvers. These benchmarks span several physical domains including weakly ionized plasma, gaseous fluids, and atomic-plasma interaction.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1995157

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 291; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (31)

Neutral Gas Transport Modeling with DEGAS 2 Stotler, Daren; Karney, Charles Contributions to Plasma Physics, Vol. 34, Issue 2-3 https://doi.org/10.1002/ctpp.2150340246	journal	January 1994
LXCat: an Open-Access, Web-Based Platform for Data Needed for Modeling Low Temperature Plasmas: LXCat: an Open-Access, Web-Based Platform for… Pitchford, Leanne C.; Alves, Luis L.; Bartschat, Klaus Plasma Processes and Polymers, Vol. 14, Issue 1-2 https://doi.org/10.1002/ppap.201600098	journal	September 2016
Values of the nodes and weights of ninth to seventeenth order gauss-markov quadrature formulae invariant under the octahedron group with inversion Lebedev, V. I. USSR Computational Mathematics and Mathematical Physics, Vol. 15, Issue 1 https://doi.org/10.1016/0041-5553(75)90133-0	journal	January 1975
A high order space–momentum discontinuous Galerkin method for the Boltzmann equation Kitzler, G.; Schöberl, J. Computers & Mathematics with Applications, Vol. 70, Issue 7 https://doi.org/10.1016/j.camwa.2015.06.011	journal	October 2015
Discontinuous Galerkin algorithms for fully kinetic plasmas Juno, J.; Hakim, A.; TenBarge, J. Journal of Computational Physics, Vol. 353 https://doi.org/10.1016/j.jcp.2017.10.009	journal	January 2018
Galerkin–Petrov approach for the Boltzmann equation Gamba, Irene M.; Rjasanow, Sergej Journal of Computational Physics, Vol. 366 https://doi.org/10.1016/j.jcp.2018.04.017	journal	August 2018
A fast spectral method for the inelastic Boltzmann collision operator and application to heated granular gases Hu, Jingwei; Ma, Zheng Journal of Computational Physics, Vol. 385 https://doi.org/10.1016/j.jcp.2019.01.049	journal	May 2019
On coupling fluid plasma and kinetic neutral physics models Joseph, I.; Rensink, M. E.; Stotler, D. P. Nuclear Materials and Energy, Vol. 12 https://doi.org/10.1016/j.nme.2017.02.021	journal	August 2017
The Boltzmann equation from quantum field theory Drewes, Marco; Mendizabal, Sebastián; Weniger, Christoph Physics Letters B, Vol. 718, Issue 3 https://doi.org/10.1016/j.physletb.2012.11.046	journal	January 2013
Electron- and photon-impact atomic ionisation Bray, I.; Fursa, D. V.; Kadyrov, A. S. Physics Reports, Vol. 520, Issue 3 https://doi.org/10.1016/j.physrep.2012.07.002	journal	November 2012
Divertor plasma detachment Krasheninnikov, S. I.; Kukushkin, A. S.; Pshenov, A. A. Physics of Plasmas, Vol. 23, Issue 5 https://doi.org/10.1063/1.4948273	journal	May 2016
Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices Hakim, Ammar H.; Mandell, Noah R.; Bernard, T. N. Physics of Plasmas, Vol. 27, Issue 4 https://doi.org/10.1063/1.5141157	journal	April 2020
Kinetic modeling of neutral transport for a continuum gyrokinetic code Bernard, T. N.; Halpern, F. D.; Francisquez, M. Physics of Plasmas, Vol. 29, Issue 5 https://doi.org/10.1063/5.0087131	journal	May 2022
A Fourier spectral method for homogeneous boltzmann equations Pareschi, Lorenzo; Perthame, Benoit Transport Theory and Statistical Physics, Vol. 25, Issue 3-5 https://doi.org/10.1080/00411459608220707	journal	April 1996
A multi-term Boltzmann equation analysis of electron swarms in gases Yachi, S.; Kitamura, Y.; Kitamori, K. Journal of Physics D: Applied Physics, Vol. 21, Issue 6 https://doi.org/10.1088/0022-3727/21/6/009	journal	June 1988
Effect of neutral transport on ITER divertor performance Kukushkin, A. S.; Pacher, H. D.; Kotov, V. Nuclear Fusion, Vol. 45, Issue 7 https://doi.org/10.1088/0029-5515/45/7/008	journal	June 2005
Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models Hagelaar, G. J. M.; Pitchford, L. C. Plasma Sources Science and Technology, Vol. 14, Issue 4 https://doi.org/10.1088/0963-0252/14/4/011	journal	October 2005
Basic physical processes and reduced models for plasma detachment Stangeby, P. C. Plasma Physics and Controlled Fusion, Vol. 60, Issue 4 https://doi.org/10.1088/1361-6587/aaacf6	journal	March 2018
The IST-LISBON database on LXCat Alves, L. L. Journal of Physics: Conference Series, Vol. 565 https://doi.org/10.1088/1742-6596/565/1/012007	journal	December 2014
Analysis of spectral methods for the homogeneous Boltzmann equation Filbet, Francis; Mouhot, Clément Transactions of the American Mathematical Society, Vol. 363, Issue 04 https://doi.org/10.1090/S0002-9947-2010-05303-6	journal	April 2011
Velocity Distributions for Elastically Colliding Electrons Morse, Philip M.; Allis, W. P.; Lamar, E. S. Physical Review, Vol. 48, Issue 5 https://doi.org/10.1103/PhysRev.48.412	journal	September 1935
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems Bhatnagar, P. L.; Gross, E. P.; Krook, M. Physical Review, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRev.94.511	journal	May 1954
Extended Boltzmann analysis of electron swarm experiments Pitchford, L. C.; ONeil, S. V.; Rumble, J. R. Physical Review A, Vol. 23, Issue 1 https://doi.org/10.1103/PhysRevA.23.294	journal	January 1981
The Distribution of Velocities in a Slightly Non-Uniform Gas Burnett, D. Proceedings of the London Mathematical Society, Vol. s2-39, Issue 1 https://doi.org/10.1112/plms/s2-39.1.385	journal	January 1935
The Distribution of Molecular Velocities and the Mean Motion in a Non-Uniform Gas Burnett, D. Proceedings of the London Mathematical Society, Vol. s2-40, Issue 1 https://doi.org/10.1112/plms/s2-40.1.382	journal	January 1936
Deterministic and stochastic modeling of rarefied gas flows in fusion particle exhaust systems Tantos, Christos; Varoutis, Stylianos; Day, Christian Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, Vol. 38, Issue 6 https://doi.org/10.1116/6.0000491	journal	September 2020
Two Pairs of Families of Estimators for Transport Problems Spanier, J. SIAM Journal on Applied Mathematics, Vol. 14, Issue 4 https://doi.org/10.1137/0114059	journal	July 1966
Solving the Boltzmann Equation in N log ₂ N Filbet, Francis; Mouhot, Clément; Pareschi, Lorenzo SIAM Journal on Scientific Computing, Vol. 28, Issue 3 https://doi.org/10.1137/050625175	journal	January 2006
Julia: A Fresh Approach to Numerical Computing Bezanson, Jeff; Edelman, Alan; Karpinski, Stefan SIAM Review, Vol. 59, Issue 1 https://doi.org/10.1137/141000671	journal	January 2017
Direct Simulation Scheme Derived from the Boltzmann Equation. I. Monocomponent Gases Nanbu, Kenichi Journal of the Physical Society of Japan, Vol. 49, Issue 5 https://doi.org/10.1143/JPSJ.49.2042	journal	November 1980
Fully conservative spectral Galerkin–Petrov method for the inhomogeneous Boltzmann equation Keßler, Torsten; Rjasanow, Sergej Kinetic & Related Models, Vol. 12, Issue 3 https://doi.org/10.3934/krm.2019021	journal	January 2019