[Paper Review] Simulating Hydrodynamics in Cosmology with CRK-HACC

Nicholas Frontiere, J. D. Emberson+5 more|arXiv (Cornell University)|Feb 6, 2022

Computational Physics and Python Applications4 citations

TL;DR

CRK-HACC introduces a GPU-accelerated cosmological hydrodynamics simulation framework by integrating Conservative Reproducing Kernel SPH (CRKSPH) into the HACC N-body code, enabling accurate, conservative modeling of baryonic physics in large-scale structure formation. The method achieves high accuracy in idealized and cosmological tests, demonstrating self-similarity and close agreement with other solvers, enabling precise synthetic sky predictions for upcoming surveys.

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 CRKSPH. $\underline{ ext{C}}$onservative $\underline{ ext{R}}$eproducing $\underline{ ext{K}}$ernel $\underline{ ext{SPH}}$ 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.

Motivation & Objective

• To extend the HACC N-body code with a conservative, accurate hydrodynamics solver for cosmological simulations.
• To incorporate CRKSPH, a smoothed particle hydrodynamics method that exactly interpolates linear fields and enforces conservation of mass, momentum, and energy.
• To maintain HACC’s performance and scalability on GPU-accelerated supercomputers while enabling baryonic physics modeling.
• To validate the new framework across idealized hydrodynamic tests and cosmological simulations, ensuring accuracy and self-similarity.
• To support future modeling of baryonic probes such as the Sunyaev-Zel’dovich effect, weak lensing, and the Lyman-alpha forest.

Proposed method

• Integrates CRKSPH, a modern SPH formulation with reproducing kernel smoothing functions that exactly interpolate linear fields.
• Preserves conservation laws (mass, momentum, energy) through a consistent, conservative discretization of the hydrodynamic equations.
• Adapts the HACC framework’s hybrid CPU-GPU architecture to scale efficiently on modern supercomputers, maintaining its performance design principles.
• Implements cosmological initial conditions with proper perturbation ordering and redshift starting points, including multi-species and massive neutrino extensions.
• Uses adaptive particle refinement and Lagrangian particle tracking to naturally resolve high-density regions in the evolving cosmological fluid.
• Incorporates subgrid models for galaxy formation and future extensions for radiative cooling and neutrino physics.

Experimental results

Research questions

• RQ1 Can CRKSPH be successfully integrated into the HACC framework to enable large-scale cosmological hydrodynamics simulations with high accuracy and performance?
• RQ2 How well does CRK-HACC reproduce known hydrodynamic benchmarks, such as the Sod shock tube and Sedov blast wave?
• RQ3 Does CRK-HACC maintain self-similarity in scale-free cosmological simulations, as predicted by theory?
• RQ4 How does CRK-HACC compare to other modern SPH and Eulerian solvers in cluster formation and halo properties, especially without artificial conductivity?
• RQ5 To what extent does the CRKSPH method improve upon traditional SPH in preserving conservation laws and reducing numerical artifacts?

Key findings

• CRK-HACC successfully reproduces idealized hydrodynamic tests, including the Sod shock tube and Sedov blast wave, with high accuracy and minimal numerical diffusion.
• The code demonstrates close agreement with other modern SPH and Eulerian solvers in cluster formation simulations, even without artificial conductivity, validating its robustness.
• Self-similarity in scale-free cosmological simulations is confirmed for key structure-forming quantities such as halo mass functions and density profiles.
• The CRKSPH method preserves conservation of mass, momentum, and energy to high precision, as required for accurate cosmological modeling.
• The framework maintains strong scaling performance on GPU-accelerated supercomputers, enabling large-volume (Gpc-scale) simulations with high dynamic range.
• Validation results support the use of CRK-HACC for generating precise synthetic sky catalogs for upcoming observational surveys, including those sensitive to baryonic effects.