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

Authors:
ORCiD logo; ;
Publication Date:
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1347623
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 318; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-04 15:15:39; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Taitano, W. T., Chacón, L., and Simakov, A. N. An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes. United States: N. p., 2016. Web. doi:10.1016/j.jcp.2016.03.071.
Taitano, W. T., Chacón, L., & Simakov, A. N. An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes. United States. doi:10.1016/j.jcp.2016.03.071.
Taitano, W. T., Chacón, L., and Simakov, A. N. 2016. "An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes". United States. doi:10.1016/j.jcp.2016.03.071.
@article{osti_1347623,
title = {An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes},
author = {Taitano, W. T. and Chacón, L. and Simakov, A. N.},
abstractNote = {},
doi = {10.1016/j.jcp.2016.03.071},
journal = {Journal of Computational Physics},
number = C,
volume = 318,
place = {United States},
year = 2016,
month = 8
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.jcp.2016.03.071

Citation Metrics:
Cited by: 3works
Citation information provided by
Web of Science

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  • Energy-conservative implicit integration schemes for the Fokker-Planck transport equation in multidimensional geometries require inverting a dense, non-symmetric matrix (Jacobian), which is very expensive to store and solve using standard solvers. However, these limitations can be overcome with Newton-Krylov iterative techniques, since they can be implemented Jacobian-free (the Jacobian matrix from Newton's algorithm is never formed nor stored to proceed with the iteration), and their convergence can be accelerated by preconditioning the original problem. In this document, the efficient numerical implementation of an implicit energy-conservative scheme for multidimensional Fokker-Planck problems using multigrid-preconditioned Krylov methods is discussed. Results show that multigrid preconditioningmore » is very effective in speeding convergence and decreasing CPU requirements, particularly in fine meshes. The solver is demonstrated on grids up to 128 x 128 points in a 2D cylindrical velocity space ({upsilon}{sub r}, {upsilon}{sub p}) with implicit time steps of the order of the collisional time scale of the problem, {tau}. The method preserves particles exactly, and energy conservation is improved over alternative approaches, particularly in coarse meshes. Typical errors in the total energy over a time period of 10{tau} remain below a percent.« less
  • Cited by 12
  • To study the kinetic physics of High-Energy-Density Laboratory Plasmas, we have developed the parallel relativistic 2D3P Vlasov-Fokker-Planck code Oshun. The numerical scheme uses a Cartesian mesh in configuration-space and incorporates a spherical harmonic expansion of the electron distribution function in momentum-space. The expansion is truncated such that the necessary angular resolution of the distribution function is retained for a given problem. Finite collisionality causes rapid decay of the high-order harmonics, thereby providing a natural truncation mechanism for the expansion. The code has both fully explicit and implicit field-solvers and employs a linearized Fokker-Planck collision operator. Oshun has been benchmarked againstmore » well-known problems, in the highly kinetic limit to model collisionless relativistic instabilities, and in the hydrodynamic limit to recover transport coefficients. The performance of the code, its applicability, and its limitations are discussed in the context of simple problems with relevance to inertial fusion energy.« less
  • We present fast numerical algorithms to solve the nonlinear Fokker-Planck-Landau equation in 3D velocity space. The discretization of the collision operator preserves the properties required by the physical nature of the Fokker-Planck-Landau equation, such as the conservation of mass, momentum, and energy, the decay of the entropy, and the fact that the steady states are Maxwellians. At the end of this paper, we give numerical results illustrating the efficiency of these fast algorithms in terms of accuracy and CPU time. 20 refs., 7 figs.