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

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

doi:10.1016/j.jcp.2018.03.007

Title: 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

DOI:https://doi.org/10.1016/j.jcp.2018.03.007· OSTI ID:1469536

^[1];

^[1]

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

We consider a 1D-2V Vlasov–Fokker–Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391–420, (2016)] to a spatially inhomogeneous system. Here in this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker–Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties 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 Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1469536

Alternate ID(s):: OSTI ID: 1548526

Report Number(s):: LA-UR-17-26086

Journal Information:: Journal of Computational Physics, Vol. 365, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 11 works

Citation information provided by
Web of Science

References (22)

Fokker-Planck Equation for an Inverse-Square Force Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L. Physical Review, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRev.107.1	journal	July 1957
On the existence of a generalized solution of Landau's equation Arsen'ev, A. A.; Peskov, N. V. USSR Computational Mathematics and Mathematical Physics, Vol. 17, Issue 4 https://doi.org/10.1016/0041-5553(77)90125-2	journal	January 1977
On asymptotics of the Boltzmann equation when the collisions become grazing Desvillettes, L. Transport Theory and Statistical Physics, Vol. 21, Issue 3 https://doi.org/10.1080/00411459208203923	journal	June 1992
On boltzmann equations and fokker—planck asymptotics: Influence of grazing collisions Goudon, T. Journal of Statistical Physics, Vol. 89, Issue 3-4 https://doi.org/10.1007/BF02765543	journal	November 1997
An efficient explicit numerical scheme for diffusion-type equations with a highly inhomogeneous and highly anisotropic diffusion tensor Larroche, O. Journal of Computational Physics, Vol. 223, Issue 1 https://doi.org/10.1016/j.jcp.2006.09.016	journal	April 2007
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
Block-structured grids for Eulerian gyrokinetic simulations Jarema, D.; Bungartz, H. J.; Görler, T. Computer Physics Communications, Vol. 198 https://doi.org/10.1016/j.cpc.2015.09.007	journal	January 2016
Fokker–Planck kinetic modeling of suprathermal α -particles in a fusion plasma Peigney, B. E.; Larroche, O.; Tikhonchuk, V. Journal of Computational Physics, Vol. 278 https://doi.org/10.1016/j.jcp.2014.08.033	journal	December 2014
Ion Fokker-Planck simulation of D- ³ He gas target implosions Larroche, O. Physics of Plasmas, Vol. 19, Issue 12 https://doi.org/10.1063/1.4771880	journal	December 2012
Species separation and modification of neutron diagnostics in inertial-confinement fusion Inglebert, A.; Canaud, B.; Larroche, O. EPL (Europhysics Letters), Vol. 107, Issue 6 https://doi.org/10.1209/0295-5075/107/65003	journal	September 2014
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
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
Electron transport in a collisional plasma with multiple ion species Simakov, Andrei N.; Molvig, Kim Physics of Plasmas, Vol. 21, Issue 2 https://doi.org/10.1063/1.4867183	journal	February 2014
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
Minimal stencil finite volume scheme with the discrete maximum principle Lipnikov, K.; Svyatskiy, D.; Vassilevski, Yu. Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 27, Issue 4 https://doi.org/10.1515/rnam-2012-0020	journal	January 2012
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
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
A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma Valentini, F.; Trávníček, P.; Califano, F. Journal of Computational Physics, Vol. 225, Issue 1 https://doi.org/10.1016/j.jcp.2007.01.001	journal	July 2007
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
Alternating direction implicit type preconditioners for the steady state inhomogeneous Vlasov equation Gasteiger, Markus; Einkemmer, Lukas; Ostermann, Alexander Journal of Plasma Physics, Vol. 83, Issue 1 https://doi.org/10.1017/s0022377817000101	journal	February 2017
Kinetic simulation of a collisional shock wave in a plasma Casanova, Michel; Larroche, Olivier; Matte, Jean-Pierre Physical Review Letters, Vol. 67, Issue 16 https://doi.org/10.1103/physrevlett.67.2143	journal	October 1991
The Fokker-Planck Asymptotics of the Boltzmann Collision Operator in the Coulomb case Degond, P.; Lucquin-Desreux, B. Mathematical Models and Methods in Applied Sciences, Vol. 02, Issue 02 https://doi.org/10.1142/s0218202592000119	journal	June 1992

Cited By (2)

Measurements of ion velocity separation and ionization in multi-species plasma shocks Rinderknecht, Hans G.; Park, H. -S.; Ross, J. S. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5023383	journal	May 2018
Nuclear yield reduction in inertial confinement fusion exploding-pusher targets explained by fuel-pusher mixing through hybrid kinetic-fluid modeling Larroche, O.; Rinderknecht, H. G.; Rosenberg, M. J. Physical Review E, Vol. 98, Issue 3 https://doi.org/10.1103/physreve.98.031201	journal	September 2018

Similar Records

A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver

Journal Article · Thu Aug 13 00:00:00 EDT 2020 · Computer Physics Communications · OSTI ID:1469536

Taitano, William; Chacon, Luis; Simakov, Andrei N.; +1 more

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 · OSTI ID:1469536

Anderson, S. E.; Taitano, W. T.; Chacón, L.; +1 more

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes

Journal Article · Mon Apr 25 00:00:00 EDT 2016 · Journal of Computational Physics · OSTI ID:1469536

Taitano, William; Chacon, Luis; Simakov, Andrei Nikolaevich

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Conservative discretization
Thermal velocity based adaptive grid
1D2V
Fokker–Planck
Rosenbluth potentials

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

Citation Formats

References (22)

Cited By (2)

Similar Records

Related Subjects