An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

Anderson, S. E.; Taitano, W. T.; Chacón, L.; Simakov, A. N.

doi:10.1016/j.jcp.2020.109686

Title: An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

Journal Article · Mon Jun 29 00:00:00 EDT 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109686· OSTI ID:1638628

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

In this paper, we consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1638628

Alternate ID(s):: OSTI ID: 1775910

Report Number(s):: LA-UR-19-24425; TRN: US2201789

Journal Information:: Journal of Computational Physics, Vol. 419, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (45)

Ion species stratification within strong shocks in two-ion plasmas Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T. Physics of Plasmas, Vol. 25, Issue 3 https://doi.org/10.1063/1.5020156	journal	March 2018
An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry Taitano, W. T.; Chacón, L.; Simakov, A. N. Journal of Computational Physics, Vol. 339 https://doi.org/10.1016/j.jcp.2017.03.032	journal	June 2017
Equation Free Projective Integration: A multiscale method applied to a plasma ion acoustic wave Shay, M. A.; Drake, J. F.; Dorland, B. Journal of Computational Physics, Vol. 226, Issue 1 https://doi.org/10.1016/j.jcp.2007.04.016	journal	September 2007
An asymptotic preserving scheme for kinetic models with singular limit Chertock, Alina; Tan, Changhui; Yan, Bokai Kinetic & Related Models, Vol. 11, Issue 4 https://doi.org/10.3934/krm.2018030	journal	January 2018
Asymptotic-Preserving methods and multiscale models for plasma physics Degond, Pierre; Deluzet, Fabrice Journal of Computational Physics, Vol. 336 https://doi.org/10.1016/j.jcp.2017.02.009	journal	May 2017
A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov–Poisson equations Rossmanith, James A.; Seal, David C. Journal of Computational Physics, Vol. 230, Issue 16 https://doi.org/10.1016/j.jcp.2011.04.018	journal	July 2011
Ion-kinetic simulations of D- ³ He gas-filled inertial confinement fusion target implosions with moderate to large Knudsen number Larroche, O.; Rinderknecht, H. G.; Rosenberg, M. J. Physics of Plasmas, Vol. 23, Issue 1 https://doi.org/10.1063/1.4939025	journal	January 2016
An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes Taitano, W. T.; Chacón, L.; Simakov, A. N. Journal of Computational Physics, Vol. 318 https://doi.org/10.1016/j.jcp.2016.03.071	journal	August 2016
Kinetic simulations of fuel ion transport in ICF target implosions Larroche, O. The European Physical Journal D - Atomic, Molecular and Optical Physics, Vol. 27, Issue 2 https://doi.org/10.1140/epjd/e2003-00251-1	journal	November 2003
An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm Chen, G.; Chacón, L.; Barnes, D. C. Journal of Computational Physics, Vol. 230, Issue 18 https://doi.org/10.1016/j.jcp.2011.05.031	journal	August 2011
A method for incorporating Gauss' law into electromagnetic PIC codes Marder, Barry Journal of Computational Physics, Vol. 68, Issue 1 https://doi.org/10.1016/0021-9991(87)90043-X	journal	January 1987
A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm Chen, G.; Chacón, L. Computer Physics Communications, Vol. 197 https://doi.org/10.1016/j.cpc.2015.08.008	journal	December 2015
A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation Taitano, W. T.; Chacón, L.; Simakov, A. N. Journal of Computational Physics, Vol. 297 https://doi.org/10.1016/j.jcp.2015.05.025	journal	September 2015
A New Code for Electrostatic Simulation by Numerical Integration of the Vlasov and Ampère Equations Using MacCormack's Method Horne, Richard B.; Freeman, Mervyn P. Journal of Computational Physics, Vol. 171, Issue 1 https://doi.org/10.1006/jcph.2001.6781	journal	July 2001
A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes Schurtz, G. P.; Nicolaï, Ph. D.; Busquet, M. Physics of Plasmas, Vol. 7, Issue 10 https://doi.org/10.1063/1.1289512	journal	January 2000
Quadratic conservative scheme for relativistic Vlasov–Maxwell system Shiroto, Takashi; Ohnishi, Naofumi; Sentoku, Yasuhiko Journal of Computational Physics, Vol. 379 https://doi.org/10.1016/j.jcp.2018.10.041	journal	February 2019
Multiscale high-order/low-order (HOLO) algorithms and applications Chacón, L.; Chen, G.; Knoll, D. A. Journal of Computational Physics, Vol. 330 https://doi.org/10.1016/j.jcp.2016.10.069	journal	February 2017
Ion kinetic dynamics in strongly-shocked plasmas relevant to ICF Rinderknecht, H. G.; Amendt, P. A.; Rosenberg, M. J. Nuclear Fusion, Vol. 57, Issue 6 https://doi.org/10.1088/1741-4326/aa69d9	journal	April 2017
Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects Taitano, William T.; Chacón, Luis Journal of Computational Physics, Vol. 284 https://doi.org/10.1016/j.jcp.2014.12.038	journal	March 2015
Curvature-compensated convective transport: SMART, A new boundedness- preserving transport algorithm Gaskell, P. H.; Lau, A. K. C. International Journal for Numerical Methods in Fluids, Vol. 8, Issue 6 https://doi.org/10.1002/fld.1650080602	journal	June 1988
Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part II: Collisional aspects Taitano, William T.; Knoll, Dana A.; Chacón, Luis Journal of Computational Physics, Vol. 284 https://doi.org/10.1016/j.jcp.2014.09.004	journal	March 2015
A rescaling velocity method for dissipative kinetic equations. Applications to granular media Filbet, Francis; Rey, Thomas Journal of Computational Physics, Vol. 248 https://doi.org/10.1016/j.jcp.2013.04.023	journal	September 2013
Moment-Based Acceleration for Neutral Gas Kinetics with BGK Collision Operator Taitano, William T.; Knoll, Dana A.; Chacón, Luis Journal of Computational and Theoretical Transport, Vol. 43, Issue 1-7 https://doi.org/10.1080/00411450.2014.910228	journal	July 2014
Yield degradation in inertial-confinement-fusion implosions due to shock-driven kinetic fuel-species stratification and viscous heating Taitano, W. T.; Simakov, A. N.; Chacón, L. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5024402	journal	May 2018
Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations Chen, G.; Chacón, L.; Leibs, C. A. Journal of Computational Physics, Vol. 258 https://doi.org/10.1016/j.jcp.2013.10.052	journal	February 2014
Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System Taitano, William T.; Knoll, Dana A.; Chacón, Luis SIAM Journal on Scientific Computing, Vol. 35, Issue 5 https://doi.org/10.1137/120881385	journal	January 2013
A Flexible Inner-Outer Preconditioned GMRES Algorithm Saad, Youcef SIAM Journal on Scientific Computing, Vol. 14, Issue 2 https://doi.org/10.1137/0914028	journal	March 1993
Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space Besse, N.; Sonnendrücker, E. Journal of Computational Physics, Vol. 191, Issue 2 https://doi.org/10.1016/S0021-9991(03)00318-8	journal	November 2003
A stable and accurate convective modelling procedure based on quadratic upstream interpolation Leonard, B. P. Computer Methods in Applied Mechanics and Engineering, Vol. 19, Issue 1 https://doi.org/10.1016/0045-7825(79)90034-3	journal	June 1979
High Order Semi-implicit Schemes for Time Dependent Partial Differential Equations Boscarino, Sebastiano; Filbet, Francis; Russo, Giovanni Journal of Scientific Computing, Vol. 68, Issue 3 https://doi.org/10.1007/s10915-016-0168-y	journal	January 2016
Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry Knoll, D. A.; Park, H.; Smith, Kord Nuclear Science and Engineering, Vol. 167, Issue 2 https://doi.org/10.13182/NSE09-75	journal	February 2011
The integration of the vlasov equation in configuration space Cheng, C. Z.; Knorr, Georg Journal of Computational Physics, Vol. 22, Issue 3 https://doi.org/10.1016/0021-9991(76)90053-X	journal	November 1976
Charge conservation in electromagnetic PIC codes; spectral comparison of Boris/DADI and Langdon-Marder methods Mardahl, P. J.; Verboncoeur, J. P. Computer Physics Communications, Vol. 106, Issue 3 https://doi.org/10.1016/S0010-4655(97)00094-5	journal	November 1997
Leveraging Anderson Acceleration for improved convergence of iterative solutions to transport systems Willert, Jeffrey; Taitano, William T.; Knoll, Dana Journal of Computational Physics, Vol. 273 https://doi.org/10.1016/j.jcp.2014.05.015	journal	September 2014
Structure and structure-preserving algorithms for plasma physics Morrison, P. J. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982054	journal	April 2017
Efficient Implementation of Weighted ENO Schemes Jiang, Guang-Shan; Shu, Chi-Wang Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0130	journal	June 1996
Kinetic physics in ICF: present understanding and future directions Rinderknecht, Hans G.; Amendt, P. A.; Wilks, S. C. Plasma Physics and Controlled Fusion, Vol. 60, Issue 6 https://doi.org/10.1088/1361-6587/aab79f	journal	April 2018
A Consistent, Moment-Based, Multiscale Solution Approach for Thermal Radiative Transfer Problems Park, H.; Knoll, D. A.; Rauenzahn, R. M. Transport Theory and Statistical Physics, Vol. 41, Issue 3-4 https://doi.org/10.1080/00411450.2012.671224	journal	May 2012
Gauss's Law satisfying Energy-Conserving Semi-Implicit Particle-in-Cell method Chen, Yuxi; Tóth, Gábor Journal of Computational Physics, Vol. 386 https://doi.org/10.1016/j.jcp.2019.02.032	journal	June 2019
An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry Taitano, W. T.; Chacón, L.; Simakov, A. N. Journal of Computational Physics, Vol. 365 https://doi.org/10.1016/j.jcp.2018.03.007	journal	July 2018
Anderson Acceleration for Fixed-Point Iterations Walker, Homer F.; Ni, Peng SIAM Journal on Numerical Analysis, Vol. 49, Issue 4 https://doi.org/10.1137/10078356X	journal	January 2011
Nonlocal Heat Transport Due to Steep Temperature Gradients Luciani, J. F.; Mora, P.; Virmont, J. Physical Review Letters, Vol. 51, Issue 18 https://doi.org/10.1103/PhysRevLett.51.1664	journal	October 1983
Energy-conserving discontinuous Galerkin methods for the Vlasov–Maxwell system Cheng, Yingda; Christlieb, Andrew J.; Zhong, Xinghui Journal of Computational Physics, Vol. 279 https://doi.org/10.1016/j.jcp.2014.08.041	journal	December 2014
Iterative Procedures for Nonlinear Integral Equations Anderson, Donald G. Journal of the ACM, Vol. 12, Issue 4 https://doi.org/10.1145/321296.321305	journal	October 1965
Vlasov and Drift Kinetic Simulation Methods Based on the Symplectic Integrator Watanabe, T. ‐H.; Sugama, H. Transport Theory and Statistical Physics, Vol. 34, Issue 3-5 https://doi.org/10.1080/00411450500274550	journal	August 2005

Similar Records

An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry

Journal Article · Mon Apr 02 00:00:00 EDT 2018 · Journal of Computational Physics · OSTI ID:1638628

Taitano, William T.; Chacon, Luis; Simakov, Andrei N.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

Journal Article · Thu Apr 05 00:00:00 EDT 2018 · SIAM Journal on Scientific Computing · OSTI ID:1638628

Garrett, C. Kristopher; Hauck, Cory D.

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics

Journal Article · Wed Nov 28 00:00:00 EST 2018 · Shock Waves · OSTI ID:1638628

Nourgaliev, R.; Greene, P.; Weston, B.; +4 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Conservative discretization
Vlasov-Ampére
adaptive velocity grid
implicit solver
high-order/low-order acceleration
HOLO

Title: An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

Citation Formats

References (45)

Similar Records

Related Subjects