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

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

doi:10.1016/j.jcp.2016.03.071

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

Abstract

In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, v_th (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v_th -ratio-based expansion of the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.

Authors:

^[1];

^[1]

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

Publication Date:: Mon Apr 25 00:00:00 EDT 2016

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

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1457268

Alternate Identifier(s):: OSTI ID: 1347623

Report Number(s):: LA-UR-15-27477
Journal ID: ISSN 0021-9991; TRN: US1901341

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 318; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Conservative discretization; thermal velocity based adaptive grid; Fokker-Planck; Rosenbluth potentials; asymptotics

Citation Formats


                    Taitano, William, Chacon, Luis, and Simakov, Andrei Nikolaevich. 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.

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                    Taitano, William, Chacon, Luis, & Simakov, Andrei Nikolaevich. An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes.  United States.  https://doi.org/10.1016/j.jcp.2016.03.071

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                    Taitano, William, Chacon, Luis, and Simakov, Andrei Nikolaevich. Mon .  
"An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes".  United States.  https://doi.org/10.1016/j.jcp.2016.03.071.  https://www.osti.gov/servlets/purl/1457268.

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@article{osti_1457268,

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

  author       = {Taitano, William and Chacon, Luis and Simakov, Andrei Nikolaevich},

  abstractNote = {In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, vth (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic vth -ratio-based expansion of the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.},

  doi          = {10.1016/j.jcp.2016.03.071},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 318,

  place        = {United States},

  year         = {Mon Apr 25 00:00:00 EDT 2016},

  month        = {Mon Apr 25 00:00:00 EDT 2016}

}

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Works referenced in this record:

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Fokker–Planck kinetic modeling of suprathermal α -particles in a fusion plasma
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Observation of early shell-dopant mix in OMEGA direct-drive implosions and comparisons with radiation-hydrodynamic simulations
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Baumgaertel, J. A.; Bradley, P. A.; Hsu, S. C.
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Hydrodynamic instabilities in beryllium targets for the National Ignition Facility
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Yi, S. A.; Simakov, A. N.; Wilson, D. C.
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Optimized beryllium target design for indirectly driven inertial confinement fusion experiments on the National Ignition Facility
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Simakov, Andrei N.; Wilson, Douglas C.; Yi, Sunghwan A.
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A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation
journal, September 2015

Taitano, W. T.; Chacón, L.; Simakov, A. N.
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Works referencing / citing this record:

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications
journal, September 2017

Brodrick, J. P.; Kingham, R. J.; Marinak, M. M.
Physics of Plasmas, Vol. 24, Issue 9
DOI: 10.1063/1.5001079

Diffusion-driven fluid dynamics in ideal gases and plasmas
journal, June 2018

Vold, E. L.; Yin, L.; Taitano, W.
Physics of Plasmas, Vol. 25, Issue 6
DOI: 10.1063/1.5029932

Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions
journal, June 2019

Yin, L.; Albright, B. J.; Vold, E. L.
Physics of Plasmas, Vol. 26, Issue 6
DOI: 10.1063/1.5109257

Kinetic physics in ICF: present understanding and future directions
journal, April 2018

Rinderknecht, Hans G.; Amendt, P. A.; Wilks, S. C.
Plasma Physics and Controlled Fusion, Vol. 60, Issue 6
DOI: 10.1088/1361-6587/aab79f

Yield degradation in inertial-confinement-fusion implosions due to shock-driven kinetic fuel-species stratification and viscous heating
journal, May 2018

Taitano, W. T.; Simakov, A. N.; Chacón, L.
Physics of Plasmas, Vol. 25, Issue 5
DOI: 10.1063/1.5024402

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

Keenan, Brett D.; Simakov, Andrei N.; Chacón, Luis
Physical Review E, Vol. 96, Issue 5
DOI: 10.1103/physreve.96.053203

Plasma kinetic effects on interfacial mix
journal, November 2016

Yin, L.; Albright, B. J.; Taitano, W.
Physics of Plasmas, Vol. 23, Issue 11
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Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration
journal, May 2018

Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R.
Journal of Scientific Computing, Vol. 77, Issue 2
DOI: 10.1007/s10915-018-0726-6

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

Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.
Physics of Plasmas, Vol. 25, Issue 3
DOI: 10.1063/1.5020156

Plasma ion stratification by weak planar shocks
journal, September 2017

Simakov, Andrei N.; Keenan, Brett D.; Taitano, William T.
Physics of Plasmas, Vol. 24, Issue 9
DOI: 10.1063/1.4995427

Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks
text, January 2017

Keenan, Brett D.; Simakov, Andrei N.; Chacon, Luis
arXiv
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Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration
preprint, January 2017

Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R.
arXiv
DOI: 10.48550/arxiv.1707.08247

Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas
text, January 2017

Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.
arXiv
DOI: 10.48550/arxiv.1712.08663

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications
journal, September 2017

Brodrick, J. P.; Kingham, R. J.; Marinak, M. M.
Physics of Plasmas, Vol. 24, Issue 9
DOI: 10.1063/1.5001079

Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks
text, January 2017

Keenan, Brett D.; Simakov, Andrei N.; Chacon, Luis
arXiv
DOI: 10.48550/arxiv.1707.02927

Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas
text, January 2017

Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.
arXiv
DOI: 10.48550/arxiv.1712.08663

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

Abstract

Citation Formats

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

On the Connection Between a Solution of the Boltzmann Equation and a Solution of the Landau-Fokker-Planck Equation journal, February 1991

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 efficient explicit numerical scheme for diffusion-type equations with a highly inhomogeneous and highly anisotropic diffusion tensor journal, April 2007

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

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

Fokker–Planck kinetic modeling of suprathermal α -particles in a fusion plasma journal, December 2014

Ion Fokker-Planck simulation of D- 3 He gas target implosions journal, December 2012

Species separation and modification of neutron diagnostics in inertial-confinement fusion journal, September 2014

Inference of ICF implosion core mix using experimental dataand theoretical mix modeling journal, December 2009

Observation of early shell-dopant mix in OMEGA direct-drive implosions and comparisons with radiation-hydrodynamic simulations journal, May 2014

Hydrodynamic instabilities in beryllium targets for the National Ignition Facility journal, September 2014

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

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation journal, September 2015

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

Preserving monotonicity in anisotropic diffusion journal, November 2007

Kinetic simulation of a plasma collision experiment journal, August 1993

Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects journal, March 2015

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications journal, September 2017

Diffusion-driven fluid dynamics in ideal gases and plasmas journal, June 2018

Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions journal, June 2019

Kinetic physics in ICF: present understanding and future directions journal, April 2018

Yield degradation in inertial-confinement-fusion implosions due to shock-driven kinetic fuel-species stratification and viscous heating journal, May 2018

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

Plasma kinetic effects on interfacial mix journal, November 2016

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration journal, May 2018

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

Plasma ion stratification by weak planar shocks journal, September 2017

Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks text, January 2017

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration preprint, January 2017

Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas text, January 2017

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications journal, September 2017

Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks text, January 2017

Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas text, January 2017

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

On the Connection Between a Solution of the Boltzmann Equation and a Solution of the Landau-Fokker-Planck Equation
journal, February 1991

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 efficient explicit numerical scheme for diffusion-type equations with a highly inhomogeneous and highly anisotropic diffusion tensor
journal, April 2007

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

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

Fokker–Planck kinetic modeling of suprathermal α -particles in a fusion plasma
journal, December 2014

Ion Fokker-Planck simulation of D- ³ He gas target implosions
journal, December 2012

Species separation and modification of neutron diagnostics in inertial-confinement fusion
journal, September 2014

Inference of ICF implosion core mix using experimental dataand theoretical mix modeling
journal, December 2009

Observation of early shell-dopant mix in OMEGA direct-drive implosions and comparisons with radiation-hydrodynamic simulations
journal, May 2014

Hydrodynamic instabilities in beryllium targets for the National Ignition Facility
journal, September 2014

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

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation
journal, September 2015

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

Preserving monotonicity in anisotropic diffusion
journal, November 2007

Kinetic simulation of a plasma collision experiment
journal, August 1993

Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects
journal, March 2015

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications
journal, September 2017

Diffusion-driven fluid dynamics in ideal gases and plasmas
journal, June 2018

Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions
journal, June 2019

Kinetic physics in ICF: present understanding and future directions
journal, April 2018

Yield degradation in inertial-confinement-fusion implosions due to shock-driven kinetic fuel-species stratification and viscous heating
journal, May 2018

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

Plasma kinetic effects on interfacial mix
journal, November 2016

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration
journal, May 2018

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

Plasma ion stratification by weak planar shocks
journal, September 2017

Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks
text, January 2017

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration
preprint, January 2017

Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas
text, January 2017

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications
journal, September 2017

Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks
text, January 2017

Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas
text, January 2017