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Kobayashi Maskawa Institute Department of Physics, Nagoya University Chiho NONAKA

Viscous Hydrodynamics for Relativistic Heavy-Ion Collisions : Riemann Solver for Quark-Gluon Plasma. Kobayashi Maskawa Institute Department of Physics, Nagoya University Chiho NONAKA. Hydrodynamic Model: Yukinao Akamatsu , Shu-ichiro Inutsuka , Makoto Takamoto Hybrid Model:

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Kobayashi Maskawa Institute Department of Physics, Nagoya University Chiho NONAKA

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  1. ViscousHydrodynamicsfor RelativisticHeavy-IonCollisions: RiemannSolver for Quark-Gluon Plasma Kobayashi Maskawa Institute Department of Physics, Nagoya University Chiho NONAKA Hydrodynamic Model: YukinaoAkamatsu, Shu-ichiroInutsuka, Makoto Takamoto Hybrid Model: YukinaoAkamatsu, Steffen Bass, Jonah Bernhard December 5, 2013@NFQCD 2013, YITP, Kyoto

  2. Numerical Algorithm hydro hadronization freezeout collisions thermalization fluctuating initial conditions hadron based event generator hydrodynamic model Current understanding

  3. Numerical Algorithm hydro hadronization freezeout collisions thermalization fluctuating initial conditions hadron based event generator hydrodynamic model Hydrodynamic expansion Initial geometry fluctuations vn MC-Glauber, MC-KLN, MC-rcBK, IP-Glasma… Current understanding

  4. Ollitrault

  5. Event-by-event calculation! Ollitrault

  6. Event-by-event calculation! small structure Shock-wave capturing scheme Stable, less numerical viscosity Ollitrault

  7. Numerical Algorithm hydro hadronization freezeout collisions thermalization fluctuating initial conditions hadron based event generator hydrodynamic model Hydrodynamic expansion Initial geometry fluctuations vn MC-Glauber, MC-KLN, MC-rcBK, IP-Glasma… numerical method Current understanding

  8. Akamatsu, Inutsuka, CN, Takamoto: arXiv:1302.1665、J. Comp. Phys. (2014) 34 Hydrodynamic model

  9. Viscous Hydrodynamic Model • Relativistic viscous hydrodynamic equation • First order in gradient: acausality • Second order in gradient: • Israel-Stewart, Ottinger and Grmela, AdS/CFT, Grad’s 14-momentum expansion, Renomarization group • Numerical scheme • Shock-wave capturing schemes: Riemann problem • Godunov scheme: analytical solution of Riemann problem • SHASTA: the first version of Flux Corrected Transport algorithm, Song, Heinz, Pang, Victor… • Kurganov-Tadmor (KT) scheme, McGill

  10. Our Approach Takamoto and Inutsuka, arXiv:1106.1732 Akamatsu, Inutsuka, CN, Takamoto,arXiv:1302.1665 • (ideal hydro) • 1. dissipative fluid dynamics = advection + dissipation exact solution • Riemann solver: Godunov method Contact discontinuity Rarefaction wave Shock wave Two shock approximation Mignone, Plewa and Bodo, Astrophys. J. S160, 199 (2005) Rarefaction wave shock wave • 2. relaxation equation = advection + stiff equation Israel-Stewart Theory

  11. Relaxation Equation Takamoto and Inutsuka, arXiv:1106.1732 + stiff equation advection • during Dt up wind method ~constant Piecewise exact solution fast numerical scheme Numerical scheme

  12. Comparison • Analytical solution • Numerical schemes • SHASTA, KT, NT • Our scheme TL=0.4 GeV v=0 EoS: ideal gas TR=0.2 GeV v=0 10 0 Nx=100, dx=0.1, dt=0.04 Shock Tube Test : Molnar, Niemi, Rischke, Eur.Phys.J.C65,615(2010)

  13. Shocktube problem shockwave rarefaction Ideal case

  14. L1 Norm TL=0.4 GeV v=0 TR=0.2 GeV v=0 10 0 For analysis of heavy ion collisions Ncell=100: dx=0.1 fm l=10 fm Numerical dissipation: deviation from analytical solution

  15. Large DT difference TL=0.4 GeV v=0 EoS: ideal gas TR=0.172 GeV v=0 10 0 Nx=100, dx=0.1, dt=0.04 • TL=0.4 GeV, TR=0.172 GeV • SHASTA becomes unstable. • Our algorithm is stable. • SHASTA: anti diffusion term, Aad • Aad= 1 : default value, unstable • Aad=0.99: stable, more numerical dissipation

  16. L1 norm Aad=0.99 Aad=1 TL=400, TR=172 TL=400, TR=200 l=10 fm SHASTA with small Aad has large numerical dissipation

  17. Artificial and Physical Viscosities Molnar, Niemi, Rischke, Eur.Phys.J.C65,615(2010) Antidiffusionterms : artificial viscosity stability

  18. Large DT difference TL=0.4 GeV v=0 EoS: ideal gas TR=0.172 GeV v=0 10 0 Nx=100, dx=0.1, dt=0.04 • TL=0.4 GeV, TR=0.172 GeV • SHASTA becomes unstable. • Our algorithm is stable. • SHASTA: anti diffusion term, Aad • Aad= 1 : default value • Aad=0.99: stable, more numerical dissipation • Large fluctuation (ex initial conditions) • Our algorithm is stable even with small numerical dissipation.

  19. Hybrid Model

  20. Our Hybrid Model hydro hadronization freezeout collisions thermalization Fluctuating Initial conditions Hydrodynamic expansion • Freezeout process • From Hydro to particle • Final state interactions Akamatsu, Inutsuka, CN, Takamoto, arXiv:1302.1665、J. Comp. Phys. (2014) 34 hydrodynamic model MC-KLN Cornelius Oscar sampler Freezeouthypersurface finder Nara Huovinen, Petersen Ohio group • http://www.aiu.ac.jp/~ynara/mckln/ UrQMD

  21. Our Hybrid Model hydro hadronization freezeout collisions thermalization Fluctuating Initial conditions Hydrodynamic expansion • Freezeout process • From Hydro to particle • Final state interactions Akamatsu, Inutsuka, CN, Takamoto, arXiv:1302.1665、J. Comp. Phys. (2014) 34 hydrodynamic model MC-KLN Cornelius Oscar sampler Freezeouthypersurface finder Nara Huovinen, Petersen Ohio group • http://www.aiu.ac.jp/~ynara/mckln/ • Simulation setups: • Free gluon EoS • Hydro in 2D boost invariant simulation • UrQMD with |y|<0.5 UrQMD

  22. Initial Pressure Distribution Pressure (fm-4) LHC RHIC Y(fm) Y(fm) X(fm) X(fm) MC-KLN (centrality 15-20%)

  23. Time Evolution of Entropy Entropy of hydro (T>TSW=155MeV)

  24. Time Evolution of en and vn Shift the origin so that ε1=0 Eccentricity & Flow anisotropy

  25. Eccentricities vs higher harmonics vn en LHC(200 events)

  26. Eccentricities vs higher harmonics vn en RHIC (200 events)

  27. Hydro + UrQMD LHC RHIC Transverse momentum spectrum

  28. Effect of Hadronic Interaction LHC RHIC Transverse momentum distribution

  29. Higher harmonics from Hydro + UrQMD Effect of hadronic interaction

  30. Summary Importance of numerical scheme Our algorithm • We develop a state-of-the-art numerical scheme • Viscosity effect • Shock wave capturing scheme: Godunov method • Less artificial diffusion: crucial for viscosity analyses • Stable for strong shock wave • Construction of a hybrid model • Fluctuating initial conditions + Hydrodynamic evolution + UrQMD • Higher Harmonics • Time evolution, hadron interaction

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