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

Abstract

In this work, we develop a conservative configuration- and velocity-space (i.e., phase-space) moving-grid strategy for the Vlasov–Fokker–Planck (VFP) equation in a planar geometry. The velocity-space grid is normalized and shifted in terms of the thermal speed and the bulk-fluid velocity, respectively. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The resulting inertial terms in the transformed VFP equations are discretized to ensure the discrete conservation of mass, momentum, and energy. To satisfy the discrete conservation theorems in the presence of phase-space mesh motion, we employ the method of discrete nonlinear constraints – explored in previous studies – but the underlying symmetries are determined in a much more efficient manner than before. The conservative grid-adaptivity strategy provides an efficient scheme that resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity. The problems test independent components of the algorithms, as well as the integrated capability on settings relevant to inertial confinement fusion.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1772417
Alternate Identifier(s):
OSTI ID: 1809113; OSTI ID: 1823747
Report Number(s):
LA-UR-19-22284; LA-UR-19-31980
Journal ID: ISSN 0010-4655
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 258; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; iFP; Vlasov-Fokker-Planck; Conservative; Adaptive phase-space grid

Citation Formats

Taitano, William, Chacon, Luis, Simakov, Andrei N., and Anderson, Steven Edward. A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver. United States: N. p., 2020. Web. doi:10.1016/j.cpc.2020.107547.
Taitano, William, Chacon, Luis, Simakov, Andrei N., & Anderson, Steven Edward. A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver. United States. https://doi.org/10.1016/j.cpc.2020.107547
Taitano, William, Chacon, Luis, Simakov, Andrei N., and Anderson, Steven Edward. 2020. "A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver". United States. https://doi.org/10.1016/j.cpc.2020.107547. https://www.osti.gov/servlets/purl/1772417.
@article{osti_1772417,
title = {A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver},
author = {Taitano, William and Chacon, Luis and Simakov, Andrei N. and Anderson, Steven Edward},
abstractNote = {In this work, we develop a conservative configuration- and velocity-space (i.e., phase-space) moving-grid strategy for the Vlasov–Fokker–Planck (VFP) equation in a planar geometry. The velocity-space grid is normalized and shifted in terms of the thermal speed and the bulk-fluid velocity, respectively. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The resulting inertial terms in the transformed VFP equations are discretized to ensure the discrete conservation of mass, momentum, and energy. To satisfy the discrete conservation theorems in the presence of phase-space mesh motion, we employ the method of discrete nonlinear constraints – explored in previous studies – but the underlying symmetries are determined in a much more efficient manner than before. The conservative grid-adaptivity strategy provides an efficient scheme that resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity. The problems test independent components of the algorithms, as well as the integrated capability on settings relevant to inertial confinement fusion.},
doi = {10.1016/j.cpc.2020.107547},
url = {https://www.osti.gov/biblio/1772417}, journal = {Computer Physics Communications},
issn = {0010-4655},
number = ,
volume = 258,
place = {United States},
year = {2020},
month = {8}
}

Works referenced in this record:

Deciphering the kinetic structure of multi-ion plasma shocks
journal, November 2017


Ion species stratification within strong shocks in two-ion plasmas
journal, March 2018


Optimized beryllium target design for indirectly driven inertial confinement fusion experiments on the National Ignition Facility
journal, February 2014


An asymptotic preserving scheme for kinetic models with singular limit
journal, January 2018


A unified gas kinetic scheme with moving mesh and velocity space adaptation
journal, August 2012


Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh
journal, November 1966


The Fokker-Planck Asymptotics of the Boltzmann Collision Operator in the Coulomb case
journal, June 1992


Positivity-preserving scheme for two-dimensional advection–diffusion equations including mixed derivatives
journal, July 2018


Vlasov simulations on an adaptive phase-space grid
journal, December 2004


Block-structured grids for Eulerian gyrokinetic simulations
journal, January 2016


A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
journal, March 1975


Kinetic simulations of fuel ion transport in ICF target implosions
journal, November 2003


Alternating direction implicit type preconditioners for the steady state inhomogeneous Vlasov equation
journal, February 2017


Moments conservation in adaptive Vlasov solver
journal, March 2006

  • Gutnic, M.; Haefele, M.; Sonnendrücker, E.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 558, Issue 1
  • https://doi.org/10.1016/j.nima.2005.11.225

Fokker-Planck Equation for an Inverse-Square Force
journal, July 1957


Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
journal, June 1994


On the existence of a generalized solution of Landau's equation
journal, January 1977


Stability of Moving Mesh Systems of Partial Differential Equations
journal, January 1998


Curvature-compensated convective transport: SMART, A new boundedness- preserving transport algorithm
journal, June 1988


A rescaling velocity method for dissipative kinetic equations. Applications to granular media
journal, September 2013


Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators
journal, July 2020


Adaptivity with moving grids
journal, May 2009


On asymptotics of the Boltzmann equation when the collisions become grazing
journal, June 1992


On boltzmann equations and fokker—planck asymptotics: Influence of grazing collisions
journal, November 1997


An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry
journal, July 2018


Moving Mesh Methods Based on Moving Mesh Partial Differential Equations
journal, August 1994


Iterative Procedures for Nonlinear Integral Equations
journal, October 1965