A Co-moving Coordinate System for Relativistic Hydrodynamics

Abstract

The equations of relativistic hydrodynamics are transformed so that steps forward in time preserves local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to co-moving observers. Aside from the time step varying as a function of the location on the mesh, the local velocity gradient and the local density then evolve according to non-relativistic equations of motion. Analytic solutions are found for two one-dimensional cases with constant speed of sound. One solution has a Gaussian density profile when mapped into the new coordinates. That solution is analyzed for the effects of longitudinal acceleration in relativistic heavy ion collisions at RHIC, especially in regards to two-particle correlation measurements of the longitudinal size.

References in corpus (10)

• Observable implications of geometrical and dynamical aspects of freeze-out in heavy ion collisions
• Charged-Particle Pseudorapidity Distributions in Au+Au Collisions at sqrt(s_NN)=62.4 GeV
• Hydrodynamics and collective behaviour in relativistic nuclear collisions
• Smoothed Particle Hydrodynamics for Relativistic Heavy Ion Collisions
• Transverse Energy Evolution as a Test of Parton Cascade Models
• Tilted Pion Sources from Azimuthally Sensitive HBT Interferometry
• Buda-Lund hydro model for ellipsoidally symmetric fireballs and the elliptic flow at RHIC
• The effect of finite-range interactions in classical transport theory
• Rapidity dependent momentum anisotropy at RHIC
• Rapidity dependence of HBT correlation radii in non-boost invariant models

Cited by in corpus (23)

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• Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics
• Entropy flow of a perfect fluid in (1+1) hydrodynamics
• Femtoscopy in Relativistic Heavy Ion Collisions and its Relation to Bulk Properties of QCD Matter
• Dynamics of QCD Matter -- current status
• Initial energy density of $\sqrt{s}=$ 7 and 8 TeV p+p collisions at the LHC
• A potential including Heaviside function in 1+1 dimensional hydrodynamics by Landau
• Analytical Solutions of Landau (1+1)-Dimensional Hydrodynamics
• Exact (1+1)-dimensional flows of a perfect fluid
• Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows
• Exact Relativistic Ideal Hydrodynamical Solutions in (1+3)D with Longitudinal and Transverse Flows
• Viscosity, non-conformal equation of state and sound velocity in Landau hydrodynamics
• On Analytic Solutions of (1+3)D Relativistic Ideal Hydrodynamic Equations
• A non-boost-invariant solution of relativistic hydrodynamics in 1+3 dimensions
• Tsunamis, Viscosity and the HBT Puzzle
• Extending the Reach of Hydrodynamics
• Mini-jet Clustering Algorithm Using Transverse-momentum Seeds in High-energy Nuclear Collisions
• Perturbative accelerating solutions of relativistic hydrodynamics
• Viscosity at RHIC: Theory and Practice