# Modeling the Dynamics of Heavy-Ion Collisions with a Hydrodynamic Model Using a Graphics Processor

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## Abstract

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## 1. Introduction

## 2. Methodology

## 3. Results

#### 3.1. Initial Conditions

#### 3.2. Hypersurface Extraction Methods

#### 3.3. Hydrodynamics and Kinematic Description

#### 3.4. Simulation of Pb-Pb Collisions at $\sqrt{{s}_{NN}}=2.76$ TeV

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Evolution of energy density cross-section in XY plane, 30–40% most central events. (

**Left**) panel time of the initial stage 0.6 fm. (

**Right**) panel time of the final stage 9.6 fm.

**Figure 5.**Shapes of thefreeze-out hypersurface from the hydrodynamic simulations (Pb-Pb collisions at $\sqrt{{s}_{NN}}=2.76$ TeV, 0–2% most central). Red solid line result from own Hydro on GPU and the initial conditions were generated from the UrQMD, averaging over 100 events. model. Blue dashed line result based on Ref. [48] from a Hydro3p1 and initial conditions were generated from the Glissando program.

**Figure 6.**Shapes of the freeze-out hypersurface from the hydrodynamic simulations (Pb-Pb collisions at $\sqrt{{s}_{NN}}=2.76$ TeV, 0–2% most central). Red solid line represents a result from our hydrodynamic model on GPU using UrQMD model as an initial conditions generator. Left panel–averaging over 10 UrQMD events, right panel–single UrQMD event.

**Figure 7.**Distribution of the azimuth angle. Azimuth angle distribution as a result of the hydrodynamic simulation on the GPU for 2000 UrQMD events. Green dashed line is 0–2%, blue dashed line is 0–5%, and red solid line is 30–40% most central events.

**Figure 8.**Elliptic flow (${v}_{2}$) as a function transverse momentum ${p}_{T}$. Green dashed line is 0–2%, blue dashed line is 0–5%, and red solid line is 30–40% most central events (2000 events for each case).

Method | Time (s) (w/Copy Overhead) | Cells Intersections | Hypersurface Elements | % of Program Runtime (w/Copy Overhead) |
---|---|---|---|---|

Cornelius (single-threded) | 46 (46.2) | 6296765 | 6606727 | 89.1% (89.3%) |

Marching cubes (parallel) | 0.18 | 6296765 | 6669758 | 3.2% |

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**MDPI and ACS Style**

Słodkowski, M.; Setniewski, D.; Aszklar, P.; Porter-Sobieraj, J.
Modeling the Dynamics of Heavy-Ion Collisions with a Hydrodynamic Model Using a Graphics Processor. *Symmetry* **2021**, *13*, 507.
https://doi.org/10.3390/sym13030507

**AMA Style**

Słodkowski M, Setniewski D, Aszklar P, Porter-Sobieraj J.
Modeling the Dynamics of Heavy-Ion Collisions with a Hydrodynamic Model Using a Graphics Processor. *Symmetry*. 2021; 13(3):507.
https://doi.org/10.3390/sym13030507

**Chicago/Turabian Style**

Słodkowski, Marcin, Dominik Setniewski, Paweł Aszklar, and Joanna Porter-Sobieraj.
2021. "Modeling the Dynamics of Heavy-Ion Collisions with a Hydrodynamic Model Using a Graphics Processor" *Symmetry* 13, no. 3: 507.
https://doi.org/10.3390/sym13030507