Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

doi:10.1016/j.cpc.2017.01.015

Title: Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA

Abstract

Relativistic fluid dynamics is a prime component in dynamical simulations of the quark-gluon plasma created in relativistic heavy-ion collisions. Simulations of the full three-dimensional dissipative dynamics of the quark-gluon plasma with fluctuating initial conditions are computationally expensive and typically require some degree of parallelization. In this paper, we introduce a GPU implementation of the Kurganov-Tadmor algorithm which solves the 3+1d relativistic viscous hydrodynamics equations including the effects of both bulk and shear viscosities. We demonstrate that the resulting CUDA-based GPU code is approximately two orders of magnitude faster than the corresponding serial implementation of the Kurganov-Tadmor algorithm. We validate the code using (semi-)analytic tests such as the relativistic shock-tube and Gubser flow.

Authors:

Bazow, Dennis ^[1];

^[1]; Strickland, Michael ^[2]

The Ohio State Univ., Columbus, OH (United States)
Kent State Univ., Kent, OH (United States)

Publication Date:: Tue Feb 28 00:00:00 EST 2017

Research Org.:: The Ohio State Univ., Columbus, OH (United States); Kent State Univ., Kent, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)

OSTI Identifier:: 1604345

Alternate Identifier(s):: OSTI ID: 1550551

Grant/Contract Number:: SC0004286; SC0013470

Resource Type:: Accepted Manuscript

Journal Name:: Computer Physics Communications

Additional Journal Information:: Journal Volume: 225; Journal Issue: C; Journal ID: ISSN 0010-4655

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Relativistic fluid dynamics; Quark-gluon plasma; GPU; CUDA; Parallel computing

Citation Formats


                    Bazow, Dennis, Heinz, Ulrich, and Strickland, Michael. Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA.  United States: N. p., 2017. 
Web.  doi:10.1016/j.cpc.2017.01.015.

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                    Bazow, Dennis, Heinz, Ulrich, & Strickland, Michael. Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA.  United States.  https://doi.org/10.1016/j.cpc.2017.01.015

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                    Bazow, Dennis, Heinz, Ulrich, and Strickland, Michael. Tue .  
"Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA".  United States.  https://doi.org/10.1016/j.cpc.2017.01.015.  https://www.osti.gov/servlets/purl/1604345.

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@article{osti_1604345,

  title        = {Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA},

  author       = {Bazow, Dennis and Heinz, Ulrich and Strickland, Michael},

  abstractNote = {Relativistic fluid dynamics is a prime component in dynamical simulations of the quark-gluon plasma created in relativistic heavy-ion collisions. Simulations of the full three-dimensional dissipative dynamics of the quark-gluon plasma with fluctuating initial conditions are computationally expensive and typically require some degree of parallelization. In this paper, we introduce a GPU implementation of the Kurganov-Tadmor algorithm which solves the 3+1d relativistic viscous hydrodynamics equations including the effects of both bulk and shear viscosities. We demonstrate that the resulting CUDA-based GPU code is approximately two orders of magnitude faster than the corresponding serial implementation of the Kurganov-Tadmor algorithm. We validate the code using (semi-)analytic tests such as the relativistic shock-tube and Gubser flow.},

  doi          = {10.1016/j.cpc.2017.01.015},

  journal      = {Computer Physics Communications},

  number       = C,

  volume       = 225,

  place        = {United States},

  year         = {Tue Feb 28 00:00:00 EST 2017},

  month        = {Tue Feb 28 00:00:00 EST 2017}

}

Copy to clipboard

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Works referenced in this record:

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Works referencing / citing this record:

A novel parallel accelerated CRPF algorithm
journal, October 2019

Wang, Jinhua; Cao, Jie; Li, Wei
Applied Intelligence, Vol. 50, Issue 3
DOI: 10.1007/s10489-019-01534-0

Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
text, January 2017

Bemfica, Fabio S.; Disconzi, Marcelo M.; Noronha, Jorge
arXiv
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Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
text, January 2018

Denicol, Gabriel; Noronha, Jorge
arXiv
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Including off-diagonal anisotropies in anisotropic hydrodynamics
text, January 2019

Nopoush, Mohammad; Strickland, Michael
arXiv
DOI: 10.48550/arxiv.1902.03303

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Title: Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA

Abstract

Citation Formats

Transport coefficients of bulk viscous pressure in the 14-moment approximation journal, August 2014

Relative importance of second-order terms in relativistic dissipative fluid dynamics journal, April 2014

Coupling Hydrodynamics to Nonequilibrium Degrees of Freedom in Strongly Interacting Quark-Gluon Plasma journal, December 2014

Numerical tests of causal relativistic dissipative fluid dynamics journal, November 2009

Symmetric hyperbolic linear differential equations journal, May 1954

Conformal hydrodynamics in Minkowski and de Sitter spacetimes journal, May 2011

A 3 + 1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions journal, November 2014

Efficient implementation of essentially non-oscillatory shock-capturing schemes journal, August 1988

Symmetry constraints on generalizations of Bjorken flow journal, October 2010

Horizon Formation and Far-from-Equilibrium Isotropization in a Supersymmetric Yang-Mills Plasma journal, May 2009

The QCD equation of state with dynamical quarks journal, November 2010

Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium journal, August 2016

High-Order Central Schemes for Hyperbolic Systems of Conservation Laws journal, January 1999

Total-Variation-Diminishing Time Discretizations journal, November 1988

Effect of bulk viscosity on elliptic flow near the QCD phase transition journal, December 2009

Third order nonoscillatory central scheme for hyperbolic conservation laws journal, May 1998

Non-oscillatory central differencing for hyperbolic conservation laws journal, April 1990

Weak solutions of nonlinear hyperbolic equations and their numerical computation journal, February 1954

Quasinormal modes of near extremal black branes journal, December 2002

Influence of temperature-dependent shear viscosity on elliptic flow at backward and forward rapidities in ultrarelativistic heavy-ion collisions journal, October 2014

AdS/CFT correspondence, quasinormal modes, and thermal correlators in N = 4 supersymmetric Yang-Mills theory journal, June 2003

New Algorithms for Ultra-relativistic Numerical Hydrodynamics journal, March 1993

Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws journal, November 1998

Transient oscillations in a macroscopic effective theory of the Boltzmann equation journal, February 2016

Collective dynamics in high-energy proton-nucleus collisions journal, July 2013

Leading-order anisotropic hydrodynamics for central collisions journal, October 2015

Pre-equilibrium dynamics and heavy-ion observables journal, December 2016

Relativistic hydrodynamics on graphic cards journal, February 2013

Elliptic and Triangular Flow in Event-by-Event D = 3 + 1 Viscous Hydrodynamics journal, January 2011

Derivation of transient relativistic fluid dynamics from the Boltzmann equation journal, June 2012

Glauber Modeling in High-Energy Nuclear Collisions journal, November 2007

Application of the Kurganov–Levy semi-discrete numerical scheme to hyperbolic problems with nonlinear source terms journal, April 2004

Determining fundamental properties of matter created in ultrarelativistic heavy-ion collisions journal, March 2014

Second-order ( 2 + 1 ) -dimensional anisotropic hydrodynamics journal, November 2014

Origin of the relaxation time in dissipative fluid dynamics journal, April 2011

Solving the heat-flow problem with transient relativistic fluid dynamics journal, March 2014

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes journal, July 2014

(3+1)D hydrodynamic simulation of relativistic heavy-ion collisions journal, July 2010

Analytical and numerical Gubser solutions of the second-order hydrodynamics journal, April 2015

Hydrodynamic Modeling of Heavy-Ion Collisions journal, April 2013

New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection–Diffusion Equations journal, May 2000

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics journal, January 2015

The iEBE-VISHNU code package for relativistic heavy-ion collisions journal, February 2016

A novel parallel accelerated CRPF algorithm journal, October 2019

Causality and existence of solutions of relativistic viscous fluid dynamics with gravity text, January 2017

Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow text, January 2018

Including off-diagonal anisotropies in anisotropic hydrodynamics text, January 2019

Transport coefficients of bulk viscous pressure in the 14-moment approximation
journal, August 2014

Relative importance of second-order terms in relativistic dissipative fluid dynamics
journal, April 2014

Coupling Hydrodynamics to Nonequilibrium Degrees of Freedom in Strongly Interacting Quark-Gluon Plasma
journal, December 2014

Numerical tests of causal relativistic dissipative fluid dynamics
journal, November 2009

Symmetric hyperbolic linear differential equations
journal, May 1954

Conformal hydrodynamics in Minkowski and de Sitter spacetimes
journal, May 2011

A $3 + 1$ dimensional viscous hydrodynamic code for relativistic heavy ion collisions
journal, November 2014

Efficient implementation of essentially non-oscillatory shock-capturing schemes
journal, August 1988

Symmetry constraints on generalizations of Bjorken flow
journal, October 2010

Horizon Formation and Far-from-Equilibrium Isotropization in a Supersymmetric Yang-Mills Plasma
journal, May 2009

The QCD equation of state with dynamical quarks
journal, November 2010

Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium
journal, August 2016

High-Order Central Schemes for Hyperbolic Systems of Conservation Laws
journal, January 1999

Total-Variation-Diminishing Time Discretizations
journal, November 1988

Effect of bulk viscosity on elliptic flow near the QCD phase transition
journal, December 2009

Third order nonoscillatory central scheme for hyperbolic conservation laws
journal, May 1998

Non-oscillatory central differencing for hyperbolic conservation laws
journal, April 1990

Weak solutions of nonlinear hyperbolic equations and their numerical computation
journal, February 1954

Quasinormal modes of near extremal black branes
journal, December 2002

Influence of temperature-dependent shear viscosity on elliptic flow at backward and forward rapidities in ultrarelativistic heavy-ion collisions
journal, October 2014

AdS/CFT correspondence, quasinormal modes, and thermal correlators in $N = 4$ supersymmetric Yang-Mills theory
journal, June 2003

New Algorithms for Ultra-relativistic Numerical Hydrodynamics
journal, March 1993

Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
journal, November 1998

Transient oscillations in a macroscopic effective theory of the Boltzmann equation
journal, February 2016

Collective dynamics in high-energy proton-nucleus collisions
journal, July 2013

Leading-order anisotropic hydrodynamics for central collisions
journal, October 2015

Pre-equilibrium dynamics and heavy-ion observables
journal, December 2016

Relativistic hydrodynamics on graphic cards
journal, February 2013

Elliptic and Triangular Flow in Event-by-Event $D = 3 + 1$ Viscous Hydrodynamics
journal, January 2011

Derivation of transient relativistic fluid dynamics from the Boltzmann equation
journal, June 2012

Glauber Modeling in High-Energy Nuclear Collisions
journal, November 2007

Application of the Kurganov–Levy semi-discrete numerical scheme to hyperbolic problems with nonlinear source terms
journal, April 2004

Determining fundamental properties of matter created in ultrarelativistic heavy-ion collisions
journal, March 2014

Second-order $(2 + 1)$ -dimensional anisotropic hydrodynamics
journal, November 2014

Origin of the relaxation time in dissipative fluid dynamics
journal, April 2011

Solving the heat-flow problem with transient relativistic fluid dynamics
journal, March 2014

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
journal, July 2014

(3+1)D hydrodynamic simulation of relativistic heavy-ion collisions
journal, July 2010

Analytical and numerical Gubser solutions of the second-order hydrodynamics
journal, April 2015

Hydrodynamic Modeling of Heavy-Ion Collisions
journal, April 2013

New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection–Diffusion Equations
journal, May 2000

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics
journal, January 2015

The iEBE-VISHNU code package for relativistic heavy-ion collisions
journal, February 2016

A novel parallel accelerated CRPF algorithm
journal, October 2019

Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
text, January 2017

Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
text, January 2018

Including off-diagonal anisotropies in anisotropic hydrodynamics
text, January 2019