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Title: Simulating Hydrodynamics in Cosmology with CRK-HACC

Abstract

Abstract We introduce CRK-HACC, an extension of the Hardware/Hybrid Accelerated Cosmology Code (HACC), to resolve gas hydrodynamics in large-scale structure formation simulations of the universe. The new framework couples the HACC gravitational N -body solver with a modern smoothed-particle hydrodynamics (SPH) approach called conservative reproducing kernel SPH (CRKSPH). CRKSPH utilizes smoothing functions that exactly interpolate linear fields while manifestly preserving conservation laws (momentum, mass, and energy). The CRKSPH method has been incorporated to accurately model baryonic effects in cosmology simulations—an important addition targeting the generation of precise synthetic sky predictions for upcoming observational surveys. CRK-HACC inherits the codesign strategies of the HACC solver and is built to run on modern GPU-accelerated supercomputers. In this work, we summarize the primary solver components and present a number of standard validation tests to demonstrate code accuracy, including idealized hydrodynamic and cosmological setups, as well as self-similarity measurements.

Authors:
; ORCiD logo; ORCiD logo; ; ; ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Argonne National Laboratory (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility (ALCF); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC); National Science Foundation (NSF); National Aeronautics and Space Administration (NASA); Space Telescope Science Institute (STScI)
OSTI Identifier:
1916483
Alternate Identifier(s):
OSTI ID: 2203848
Grant/Contract Number:  
AC02-06CH11357; AC05-00OR22725; AC02-05CH11231; m3921; AST-1715216; AST-2108230; AST-1652522; 17-ATP17-0067; HST-AR-16124.001-A
Resource Type:
Published Article
Journal Name:
The Astrophysical Journal. Supplement Series
Additional Journal Information:
Journal Name: The Astrophysical Journal. Supplement Series Journal Volume: 264 Journal Issue: 2; Journal ID: ISSN 0067-0049
Publisher:
American Astronomical Society
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; cosmology theory; hydrodynamics; numerical methods; computational methods; hydrodynamical simulations; large-scale structure of the universe; cosmology

Citation Formats

Frontiere, Nicholas, Emberson, J. D., Buehlmann, Michael, Adamo, Joseph, Habib, Salman, Heitmann, Katrin, and Faucher-Giguère, Claude-André. Simulating Hydrodynamics in Cosmology with CRK-HACC. United States: N. p., 2023. Web. doi:10.3847/1538-4365/aca58d.
Frontiere, Nicholas, Emberson, J. D., Buehlmann, Michael, Adamo, Joseph, Habib, Salman, Heitmann, Katrin, & Faucher-Giguère, Claude-André. Simulating Hydrodynamics in Cosmology with CRK-HACC. United States. https://doi.org/10.3847/1538-4365/aca58d
Frontiere, Nicholas, Emberson, J. D., Buehlmann, Michael, Adamo, Joseph, Habib, Salman, Heitmann, Katrin, and Faucher-Giguère, Claude-André. Tue . "Simulating Hydrodynamics in Cosmology with CRK-HACC". United States. https://doi.org/10.3847/1538-4365/aca58d.
@article{osti_1916483,
title = {Simulating Hydrodynamics in Cosmology with CRK-HACC},
author = {Frontiere, Nicholas and Emberson, J. D. and Buehlmann, Michael and Adamo, Joseph and Habib, Salman and Heitmann, Katrin and Faucher-Giguère, Claude-André},
abstractNote = {Abstract We introduce CRK-HACC, an extension of the Hardware/Hybrid Accelerated Cosmology Code (HACC), to resolve gas hydrodynamics in large-scale structure formation simulations of the universe. The new framework couples the HACC gravitational N -body solver with a modern smoothed-particle hydrodynamics (SPH) approach called conservative reproducing kernel SPH (CRKSPH). CRKSPH utilizes smoothing functions that exactly interpolate linear fields while manifestly preserving conservation laws (momentum, mass, and energy). The CRKSPH method has been incorporated to accurately model baryonic effects in cosmology simulations—an important addition targeting the generation of precise synthetic sky predictions for upcoming observational surveys. CRK-HACC inherits the codesign strategies of the HACC solver and is built to run on modern GPU-accelerated supercomputers. In this work, we summarize the primary solver components and present a number of standard validation tests to demonstrate code accuracy, including idealized hydrodynamic and cosmological setups, as well as self-similarity measurements.},
doi = {10.3847/1538-4365/aca58d},
journal = {The Astrophysical Journal. Supplement Series},
number = 2,
volume = 264,
place = {United States},
year = {Tue Jan 24 00:00:00 EST 2023},
month = {Tue Jan 24 00:00:00 EST 2023}
}

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Works referenced in this record:

Astrophysical smooth particle hydrodynamics
journal, April 2009


E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh
journal, January 2010


Robustness of Cosmological Simulations. I. Large‐Scale Structure
journal, September 2005

  • Heitmann, Katrin; Ricker, Paul M.; Warren, Michael S.
  • The Astrophysical Journal Supplement Series, Vol. 160, Issue 1
  • DOI: 10.1086/432646

The Coyote Universe. i. Precision Determination of the Nonlinear Matter Power Spectrum
journal, April 2010


Radiative Transfer in a Clumpy Universe. iv. new Synthesis Models of the Cosmic Uv/X-Ray Background
journal, February 2012


Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann‐Robertson‐Walker Models
journal, August 2000

  • Lewis, Antony; Challinor, Anthony; Lasenby, Anthony
  • The Astrophysical Journal, Vol. 538, Issue 2
  • DOI: 10.1086/309179

Power spectrum for the small-scale Universe
journal, August 2009

  • Widrow, Lawrence M.; Elahi, Pascal J.; Thacker, Robert J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 397, Issue 3
  • DOI: 10.1111/j.1365-2966.2009.15075.x

The Last Journey. I. An Extreme-scale Simulation on the Mira Supercomputer
journal, January 2021

  • Heitmann, Katrin; Frontiere, Nicholas; Rangel, Esteban
  • The Astrophysical Journal Supplement Series, Vol. 252, Issue 2
  • DOI: 10.3847/1538-4365/abcc67

Chemical enrichment in cosmological, smoothed particle hydrodynamics simulations
journal, October 2009


The role of the artificial conductivity in SPH simulations of galaxy clusters: effects on the ICM properties
journal, November 2014

  • Biffi, V.; Valdarnini, R.
  • Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 3
  • DOI: 10.1093/mnras/stu2278

A moving frame algorithm for high Mach number hydrodynamics
journal, July 2004


Inviscid smoothed particle hydrodynamics: Inviscid smoothed particle hydrodynamics
journal, July 2010


Modelling feedback from stars and black holes in galaxy mergers
journal, August 2005

  • Springel, Volker; Di Matteo, Tiziana; Hernquist, Lars
  • Monthly Notices of the Royal Astronomical Society, Vol. 361, Issue 3
  • DOI: 10.1111/j.1365-2966.2005.09238.x

SPHGal: smoothed particle hydrodynamics with improved accuracy for galaxy simulations
journal, July 2014

  • Hu, Chia-Yu; Naab, Thorsten; Walch, Stefanie
  • Monthly Notices of the Royal Astronomical Society, Vol. 443, Issue 2
  • DOI: 10.1093/mnras/stu1187

On the origin of cores in simulated galaxy clusters
journal, May 2009


Smoothed Particle Hydrodynamics in Astrophysics
journal, August 2010


The effects of galaxy formation on the matter power spectrum: a challenge for precision cosmology: Galaxy formation and the matter power spectrum
journal, July 2011


An Exact Integration Scheme for Radiative Cooling in Hydrodynamical Simulations
journal, March 2009


Halo Profiles and the Concentration–Mass Relation for a ΛCDM Universe
journal, May 2018

  • Child, Hillary L.; Habib, Salman; Heitmann, Katrin
  • The Astrophysical Journal, Vol. 859, Issue 1
  • DOI: 10.3847/1538-4357/aabf95

von Neumann stability analysis of smoothed particle hydrodynamics—suggestions for optimal algorithms
journal, October 1995


On the Construction and Comparison of Difference Schemes
journal, September 1968

  • Strang, Gilbert
  • SIAM Journal on Numerical Analysis, Vol. 5, Issue 3
  • DOI: 10.1137/0705041

A numerical approach to the testing of the fission hypothesis
journal, December 1977


Resolving mixing in smoothed particle hydrodynamics: Resolving mixing in SPH
journal, May 2010


Moving-least-squares-particle hydrodynamics?I. Consistency and stability
journal, March 1999


The Tree Particle‐Mesh N ‐Body Gravity Solver
journal, June 2000

  • Bode, Paul; Ostriker, Jeremiah P.; Xu, Guohong
  • The Astrophysical Journal Supplement Series, Vol. 128, Issue 2
  • DOI: 10.1086/313398

A Switch to Reduce SPH Viscosity
journal, September 1997

  • Morris, J. P.; Monaghan, J. J.
  • Journal of Computational Physics, Vol. 136, Issue 1
  • DOI: 10.1006/jcph.1997.5690

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978


A Well-Posed Kelvin-Helmholtz Instability test and Comparison
journal, June 2012

  • McNally, Colin P.; Lyra, Wladimir; Passy, Jean-Claude
  • The Astrophysical Journal Supplement Series, Vol. 201, Issue 2
  • DOI: 10.1088/0067-0049/201/2/18

On the Mechanism of Accretion by Stars
journal, October 1944

  • Bondi, H.; Hoyle, F.
  • Monthly Notices of the Royal Astronomical Society, Vol. 104, Issue 5
  • DOI: 10.1093/mnras/104.5.273

The q Continuum Simulation: Harnessing the Power of gpu Accelerated Supercomputers
journal, August 2015

  • Heitmann, Katrin; Frontiere, Nicholas; Sewell, Chris
  • The Astrophysical Journal Supplement Series, Vol. 219, Issue 2
  • DOI: 10.1088/0067-0049/219/2/34

Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
journal, December 1995

  • Wendland, Holger
  • Advances in Computational Mathematics, Vol. 4, Issue 1
  • DOI: 10.1007/BF02123482

Multiple-scale reproducing kernel particle methods for large deformation problems
journal, April 1998


Particle hydrodynamics with tessellation techniques: Tessellation based particle hydrodynamics
journal, June 2010


Cosmological Simulations with Scale‐Free Initial Conditions. I. Adiabatic Hydrodynamics
journal, August 1998

  • Owen, J. Michael; Weinberg, David H.; Evrard, August E.
  • The Astrophysical Journal, Vol. 503, Issue 1
  • DOI: 10.1086/305957

Effects of Baryons and Dissipation on the Matter Power Spectrum
journal, January 2008

  • Rudd, Douglas H.; Zentner, Andrew R.; Kravtsov, Andrey V.
  • The Astrophysical Journal, Vol. 672, Issue 1
  • DOI: 10.1086/523836

Merger rates in hierarchical models of galaxy formation – II. Comparison with N-body simulations
journal, December 1994

  • Lacey, Cedric; Cole, Shanu
  • Monthly Notices of the Royal Astronomical Society, Vol. 271, Issue 3
  • DOI: 10.1093/mnras/271.3.676

Improving convergence in smoothed particle hydrodynamics simulations without pairing instability: SPH without pairing instability
journal, August 2012


Evolution and clustering of rich clusters
journal, September 1986


A Multiple Time Step Symplectic Algorithm for Integrating Close Encounters
journal, October 1998

  • Duncan, Martin J.; Levison, Harold F.; Lee, Man Hoi
  • The Astronomical Journal, Vol. 116, Issue 4
  • DOI: 10.1086/300541

Resolving the Structure of Cold Dark Matter Halos
journal, June 2001

  • Klypin, Anatoly; Kravtsov, Andrey V.; Bullock, James S.
  • The Astrophysical Journal, Vol. 554, Issue 2
  • DOI: 10.1086/321400

Cosmological hydrodynamics with adaptive mesh refinement: A new high resolution code called RAMSES
journal, April 2002


Higher order initial conditions for mixed baryon–CDM simulations
journal, December 2020

  • Hahn, Oliver; Rampf, Cornelius; Uhlemann, Cora
  • Monthly Notices of the Royal Astronomical Society, Vol. 503, Issue 1
  • DOI: 10.1093/mnras/staa3773

Einasto profiles and the dark matter power spectrum
journal, October 2016

  • Ludlow, Aaron D.; Angulo, Raúl E.
  • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 465, Issue 1
  • DOI: 10.1093/mnrasl/slw216

Large-scale dark matter simulations
journal, February 2022


Gravitational clustering from scale-free initial conditions
journal, December 1988

  • Efstathiou, George; Frenk, Carlos S.; White, Simon D. M.
  • Monthly Notices of the Royal Astronomical Society, Vol. 235, Issue 3
  • DOI: 10.1093/mnras/235.3.715

Farpoint: A High-resolution Cosmology Simulation at the Gigaparsec Scale
journal, February 2022

  • Frontiere, Nicholas; Heitmann, Katrin; Rangel, Esteban
  • The Astrophysical Journal Supplement Series, Vol. 259, Issue 1
  • DOI: 10.3847/1538-4365/ac43b9

N-body integrators with individual time steps from Hierarchical splitting
journal, November 2012


Stable clustering, the halo model and non-linear cosmological power spectra
journal, June 2003


Simulating galaxy formation with black hole driven thermal and kinetic feedback
journal, November 2016

  • Weinberger, Rainer; Springel, Volker; Hernquist, Lars
  • Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 3
  • DOI: 10.1093/mnras/stw2944

The Lyman α forest in optically thin hydrodynamical simulations
journal, December 2014

  • Lukić, Zarija; Stark, Casey W.; Nugent, Peter
  • Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 4
  • DOI: 10.1093/mnras/stu2377

Fourth-order symplectic integration
journal, May 1990


nIFTy galaxy cluster simulations – I. Dark matter and non-radiative models
journal, February 2016

  • Sembolini, Federico; Yepes, Gustavo; Pearce, Frazer R.
  • Monthly Notices of the Royal Astronomical Society, Vol. 457, Issue 4
  • DOI: 10.1093/mnras/stw250

Santa Barbara Cluster Comparison test with Disph
journal, June 2016


Halo concentrations in the standard Λ cold dark matter cosmology: ΛCDM halo concentrations
journal, June 2012

  • Prada, Francisco; Klypin, Anatoly A.; Cuesta, Antonio J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 423, Issue 4
  • DOI: 10.1111/j.1365-2966.2012.21007.x

Examining the Accuracy of Astrophysical disk Simulations with a Generalized Hydrodynamical test Problem
journal, October 2016


Gasoline2: a modern smoothed particle hydrodynamics code
journal, June 2017

  • Wadsley, James W.; Keller, Benjamin W.; Quinn, Thomas R.
  • Monthly Notices of the Royal Astronomical Society, Vol. 471, Issue 2
  • DOI: 10.1093/mnras/stx1643

A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems
journal, November 2012

  • Hopkins, Philip F.
  • Monthly Notices of the Royal Astronomical Society, Vol. 428, Issue 4
  • DOI: 10.1093/mnras/sts210

The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions
journal, November 1999

  • Frenk, C. S.; White, S. D. M.; Bode, P.
  • The Astrophysical Journal, Vol. 525, Issue 2
  • DOI: 10.1086/307908

Self‐Similar Evolution of Gravitational Clustering. II. N ‐Body Simulations of the n = −2 Spectrum
journal, December 1998

  • Jain, Bhuvnesh; Bertschinger, Edmund
  • The Astrophysical Journal, Vol. 509, Issue 2
  • DOI: 10.1086/306538

SPHS: smoothed particle hydrodynamics with a higher order dissipation switch: SPH with a higher order dissipation switch
journal, April 2012


Hybrid petacomputing meets cosmology: The Roadrunner Universe project
journal, July 2009


The impact of baryons on the sensitivity of dark energy measurements
journal, July 2018

  • Copeland, David; Taylor, Andy; Hall, Alex
  • Monthly Notices of the Royal Astronomical Society, Vol. 480, Issue 2
  • DOI: 10.1093/mnras/sty2001

Shock simulation by the particle method SPH
journal, November 1983


The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium
journal, April 1989


How closely do baryons follow dark matter on large scales?
journal, July 2013

  • Angulo, Raul E.; Hahn, Oliver; Abel, Tom
  • Monthly Notices of the Royal Astronomical Society, Vol. 434, Issue 2
  • DOI: 10.1093/mnras/stt1135

Initial conditions for accurate N -body simulations of massive neutrino cosmologies
journal, December 2016

  • Zennaro, M.; Bel, J.; Villaescusa-Navarro, F.
  • Monthly Notices of the Royal Astronomical Society, Vol. 466, Issue 3
  • DOI: 10.1093/mnras/stw3340

The evolution of large-scale structure in a universe dominated by cold dark matter
journal, May 1985

  • Davis, M.; Efstathiou, G.; Frenk, C. S.
  • The Astrophysical Journal, Vol. 292
  • DOI: 10.1086/163168

ArborX: A Performance Portable Geometric Search Library
journal, January 2021

  • Lebrun-Grandié, D.; Prokopenko, A.; Turcksin, B.
  • ACM Transactions on Mathematical Software, Vol. 47, Issue 1
  • DOI: 10.1145/3412558

Computer Simulation Using Particles
book, January 1988


Modelling discontinuities and Kelvin–Helmholtz instabilities in SPH
journal, December 2008


Stable clustering and the resolution of dissipationless cosmological N-body simulations
journal, June 2017

  • Benhaiem, David; Joyce, Michael; Sylos Labini, Francesco
  • Monthly Notices of the Royal Astronomical Society, Vol. 470, Issue 4
  • DOI: 10.1093/mnras/stx1356

Self-similar gravitational clustering
journal, November 1979

  • Efstathiou, G.; Fall, S. M.; Hogan, C.
  • Monthly Notices of the Royal Astronomical Society, Vol. 189, Issue 2
  • DOI: 10.1093/mnras/189.2.203

Merger rates in hierarchical models of galaxy formation
journal, June 1993

  • Lacey, C.; Cole, S.
  • Monthly Notices of the Royal Astronomical Society, Vol. 262, Issue 3
  • DOI: 10.1093/mnras/262.3.627

SPHYNX: an accurate density-based SPH method for astrophysical applications
journal, October 2017


Cosmological simulations of the growth of supermassive black holes and feedback from active galactic nuclei: method and tests
journal, September 2009


A Universal Density Profile from Hierarchical Clustering
journal, December 1997

  • Navarro, Julio F.; Frenk, Carlos S.; White, Simon D. M.
  • The Astrophysical Journal, Vol. 490, Issue 2
  • DOI: 10.1086/304888

Smoothed particle hydrodynamics and magnetohydrodynamics
journal, February 2012


Cosmological simulations of black hole growth: AGN luminosities and downsizing
journal, June 2014

  • Hirschmann, M.; Dolag, K.; Saro, A.
  • Monthly Notices of the Royal Astronomical Society, Vol. 442, Issue 3
  • DOI: 10.1093/mnras/stu1023

A piecewise parabolic method for cosmological hydrodynamics
journal, August 1995


HACC: Simulating sky surveys on state-of-the-art supercomputing architectures
journal, January 2016


Quantifying resolution in cosmological N- body simulations using self-similarity
journal, November 2020

  • Joyce, Michael; Garrison, Lehman; Eisenstein, Daniel
  • Monthly Notices of the Royal Astronomical Society, Vol. 501, Issue 4
  • DOI: 10.1093/mnras/staa3434

The Outer Rim Simulation: A Path to Many-core Supercomputers
journal, November 2019

  • Heitmann, Katrin; Finkel, Hal; Pope, Adrian
  • The Astrophysical Journal Supplement Series, Vol. 245, Issue 1
  • DOI: 10.3847/1538-4365/ab4da1

The cosmological simulation code gadget-2
journal, December 2005


Effects of the initial conditions on cosmological N-body simulations
journal, July 2014


Smoothed Particle Hydrodynamics in cosmology: a comparative study of implementations
journal, December 2000


Reversible multiple time scale molecular dynamics
journal, August 1992

  • Tuckerman, M.; Berne, B. J.; Martyna, G. J.
  • The Journal of Chemical Physics, Vol. 97, Issue 3
  • DOI: 10.1063/1.463137

An improved SPH scheme for cosmological simulations
journal, November 2015

  • Beck, A. M.; Murante, G.; Arth, A.
  • Monthly Notices of the Royal Astronomical Society, Vol. 455, Issue 2
  • DOI: 10.1093/mnras/stv2443

The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes
journal, July 2011

  • Blas, Diego; Lesgourgues, Julien; Tram, Thomas
  • Journal of Cosmology and Astroparticle Physics, Vol. 2011, Issue 07
  • DOI: 10.1088/1475-7516/2011/07/034

Simulating cosmic structure formation with the gadget -4 code
journal, July 2021

  • Springel, Volker; Pakmor, Rüdiger; Zier, Oliver
  • Monthly Notices of the Royal Astronomical Society, Vol. 506, Issue 2
  • DOI: 10.1093/mnras/stab1855

TREESPH - A unification of SPH with the hierarchical tree method
journal, June 1989

  • Hernquist, Lars; Katz, Neal
  • The Astrophysical Journal Supplement Series, Vol. 70
  • DOI: 10.1086/191344

The formation of entropy cores in non-radiative galaxy cluster simulations: smoothed particle hydrodynamics versus adaptive mesh refinement
journal, April 2014

  • Power, C.; Read, J. I.; Hobbs, A.
  • Monthly Notices of the Royal Astronomical Society, Vol. 440, Issue 4
  • DOI: 10.1093/mnras/stu418

Constrained realizations of Gaussian fields - A simple algorithm
journal, October 1991

  • Hoffman, Yehuda; Ribak, Erez
  • The Astrophysical Journal, Vol. 380
  • DOI: 10.1086/186160

Cosmological simulations of galaxy formation
journal, January 2020

  • Vogelsberger, Mark; Marinacci, Federico; Torrey, Paul
  • Nature Reviews Physics, Vol. 2, Issue 1
  • DOI: 10.1038/s42254-019-0127-2

More accurate simulations with separate initial conditions for baryons and dark matter
journal, June 2020

  • Bird, Simeon; Feng, Yu; Pedersen, Christian
  • Journal of Cosmology and Astroparticle Physics, Vol. 2020, Issue 06
  • DOI: 10.1088/1475-7516/2020/06/002

FIRE-2 simulations: physics versus numerics in galaxy formation
journal, June 2018

  • Hopkins, Philip F.; Wetzel, Andrew; Kereš, Dušan
  • Monthly Notices of the Royal Astronomical Society, Vol. 480, Issue 1
  • DOI: 10.1093/mnras/sty1690

A New Parallel N-Body Gravity Solver: TPM
journal, May 1995

  • Xu, Guohong
  • The Astrophysical Journal Supplement Series, Vol. 98
  • DOI: 10.1086/192166

TreePM: A code for cosmological N-body simulations
journal, December 2002

  • Bagla, J. S.
  • Journal of Astrophysics and Astronomy, Vol. 23, Issue 3-4
  • DOI: 10.1007/BF02702282

On the clustering of particles in an expanding Universe
journal, March 1981

  • Efstathiou, G.; Eastwood, J. W.
  • Monthly Notices of the Royal Astronomical Society, Vol. 194, Issue 3
  • DOI: 10.1093/mnras/194.3.503

A new class of accurate, mesh-free hydrodynamic simulation methods
journal, April 2015

  • Hopkins, Philip F.
  • Monthly Notices of the Royal Astronomical Society, Vol. 450, Issue 1
  • DOI: 10.1093/mnras/stv195

Accurate initial conditions in mixed dark matter–baryon simulations
journal, February 2017

  • Valkenburg, Wessel; Villaescusa-Navarro, Francisco
  • Monthly Notices of the Royal Astronomical Society, Vol. 467, Issue 4
  • DOI: 10.1093/mnras/stx376

On the treatment of entropy mixing in numerical cosmology
journal, June 2008


HACC: extreme scaling and performance across diverse architectures
conference, January 2013

  • Habib, Salman; Morozov, Vitali; Frontiere, Nicholas
  • Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - SC '13
  • DOI: 10.1145/2503210.2504566

Smoothed particle hydrodynamics: theory and application to non-spherical stars
journal, December 1977

  • Gingold, R. A.; Monaghan, J. J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 181, Issue 3
  • DOI: 10.1093/mnras/181.3.375

SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: COSMOLOGICAL INTERPRETATION
journal, January 2011

  • Komatsu, E.; Smith, K. M.; Dunkley, J.
  • The Astrophysical Journal Supplement Series, Vol. 192, Issue 2
  • DOI: 10.1088/0067-0049/192/2/18

Reproducing kernel particle methods
journal, April 1995

  • Liu, Wing Kam; Jun, Sukky; Zhang, Yi Fei
  • International Journal for Numerical Methods in Fluids, Vol. 20, Issue 8-9
  • DOI: 10.1002/fld.1650200824

The Borg Cube Simulation: Cosmological Hydrodynamics with CRK-SPH
journal, May 2019

  • Emberson, J. D.; Frontiere, Nicholas; Habib, Salman
  • The Astrophysical Journal, Vol. 877, Issue 2
  • DOI: 10.3847/1538-4357/ab1b31

Smoothed particle hydrodynamics
journal, July 2005


A fast recursive coordinate bisection tree for neighbour search and gravity: A fast tree for neighbour search and gravity
journal, September 2011


A Necessary Condition for Individual time Steps in sph Simulations
journal, May 2009


Implementation of feedback in smoothed particle hydrodynamics: towards concordance of methods: Towards concordance of feedback methods in SPH
journal, October 2011


The EAGLE project: simulating the evolution and assembly of galaxies and their environments
journal, November 2014

  • Schaye, Joop; Crain, Robert A.; Bower, Richard G.
  • Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 1
  • DOI: 10.1093/mnras/stu2058

A compatibly differenced total energy conserving form of SPH: A COMPATIBLY DIFFERENCED TOTAL ENERGY CONSERVING FORM OF SPH
journal, April 2014

  • Michael Owen, J.
  • International Journal for Numerical Methods in Fluids, Vol. 75, Issue 11
  • DOI: 10.1002/fld.3912

A cosmic UV/X-ray background model update
journal, January 2020

  • Faucher-Giguère, Claude-André
  • Monthly Notices of the Royal Astronomical Society, Vol. 493, Issue 2
  • DOI: 10.1093/mnras/staa302

CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme
journal, March 2017

  • Frontiere, Nicholas; Raskin, Cody D.; Owen, J. Michael
  • Journal of Computational Physics, Vol. 332
  • DOI: 10.1016/j.jcp.2016.12.004

Simulating galaxy formation with the IllustrisTNG model
journal, October 2017

  • Pillepich, Annalisa; Springel, Volker; Nelson, Dylan
  • Monthly Notices of the Royal Astronomical Society, Vol. 473, Issue 3
  • DOI: 10.1093/mnras/stx2656

Symplectic integrators for solar system dynamics
journal, October 1992

  • Saha, Prasenjit; Tremaine, Scott
  • The Astronomical Journal, Vol. 104
  • DOI: 10.1086/116347

Fundamental differences between SPH and grid methods: Simulating fluids using SPH and grid techniques
journal, August 2007


Cardinal interpolation and spline functions
journal, June 1969


Baryons, neutrinos, feedback and weak gravitational lensing
journal, April 2015

  • Harnois-Déraps, Joachim; van Waerbeke, Ludovic; Viola, Massimo
  • Monthly Notices of the Royal Astronomical Society, Vol. 450, Issue 2
  • DOI: 10.1093/mnras/stv646

Construction of higher order symplectic integrators
journal, November 1990


Spurious haloes and discreteness-driven relaxation in cosmological simulations
journal, July 2016

  • Power, C.; Robotham, A. S. G.; Obreschkow, D.
  • Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 1
  • DOI: 10.1093/mnras/stw1644

A unified model for AGN feedback in cosmological simulations of structure formation: AGN feedback in cosmological simulations
journal, August 2007

  • Sijacki, Debora; Springel, Volker; Di Matteo, Tiziana
  • Monthly Notices of the Royal Astronomical Society, Vol. 380, Issue 3
  • DOI: 10.1111/j.1365-2966.2007.12153.x

Two-body relaxation in cosmological simulations
journal, June 2002


Theoretical Challenges in Galaxy Formation
journal, August 2017


The Halo Mass Function: High‐Redshift Evolution and Universality
journal, December 2007

  • Lukić, Zarija; Heitmann, Katrin; Habib, Salman
  • The Astrophysical Journal, Vol. 671, Issue 2
  • DOI: 10.1086/523083

FAST: A Fully Asynchronous Split Time-Integrator for a Self-Gravitating Fluid
journal, April 2010

  • Saitoh, Takayuki R.; Makino, Junichiro
  • Publications of the Astronomical Society of Japan, Vol. 62, Issue 2
  • DOI: 10.1093/pasj/62.2.301

The Accelerated Universe
journal, July 2010

  • Pope, Adrian; Habib, Salman; Lukic, Zarija
  • Computing in Science & Engineering, Vol. 12, Issue 4
  • DOI: 10.1109/MCSE.2010.28

Introducing the Illustris Project: simulating the coevolution of dark and visible matter in the Universe
journal, August 2014

  • Vogelsberger, Mark; Genel, Shy; Springel, Volker
  • Monthly Notices of the Royal Astronomical Society, Vol. 444, Issue 2
  • DOI: 10.1093/mnras/stu1536

A momentum-conserving N-body scheme with individual time steps
journal, May 2021


Cosmological smoothed particle hydrodynamics simulations: a hybrid multiphase model for star formation
journal, February 2003


Nyx: A MASSIVELY PARALLEL AMR CODE FOR COMPUTATIONAL COSMOLOGY
journal, February 2013