Relativistic Smoothed Particle Hydrodynamics

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Relativistic Smoothed Particle Hydrodynamics
C.E. Aguiar, T. Kodama U.F. Rio de Janeiro T.
Osada,Y. Hama U. São Paulo

• Outline
• Relativistic hydrodynamics
• Relativistic SPH
• Entropy-based SPH
• Shocks and artificial viscosity

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Relativistic Hydrodynamics
Energy-momentum conservation
Baryon-number conservation
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Baryon number conservation
comoving derivative
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Energy-momentum conservation
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Momentum equation
Energy equation
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Entropy conservation
s entropy density (rest frame)
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Lagrangian Equations
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SPH

• Developed to study gas dynamics in
  astrophysical systems.
• Lagrangian method.
• No grids.
• Arbitrary geometries.
• Equally applicable in 1, 2 and 3 space
• dimensions.

- L.Lucy, Astron.J. 82, 1013 (1977) - R.Gingold,
J.Monaghan, MNRAS 181, 378 (1977)
Reviews - J. Monaghan, Annu. Rev. Astron.
Astrophys. 30, 543 (1992) - L. Hernquist, N.
Katz, Ap. J. Suppl. 70, 419 (1989)
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Smoothing
h
x
0
Error
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Particles
"Monte-Carlo" sampling
nb baryon number of ''particle'' b
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Different ways of writing SP estimates (we omit
the SP subscript from now on)
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Derivatives
No need for finite differences and grids
D
D
i1
i-1
i
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More than one way of calculating derivatives
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Moving the Particles
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Momentum equation
Energy equation
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Energy and Momentum
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Entropy equation
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Particle Velocity
equation for g
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RSPH Equations
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Baryon-Free Matter
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Lagrangian equations
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Entropy-based RSPH
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Ultrarelativistic Pion Gas
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Pion Gas
Rarefaction Wave
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Pion Gas
Landau Solution
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Shock Waves
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Pion Gas
Shock Wave
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Artificial Viscosity
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Second Law of Thermodynamics
Thermodynamically normal matter
Thermodynamically anomalous matter
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(No Transcript)
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Dissipative RSPH
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Pion Gas
Shock Wave
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Pion Gas
Rankine - Hugoniot
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QGP Pion Gas
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QGP Pions
Rarefaction Shock
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QGP Pions
Rarefaction Shock
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QGP Pions
Rarefaction Shock