Analytical Solutions of Landau (1+1)-Dimensional Hydrodynamics

Abstract

To help guide our intuition, summarize important features, and point out essential elements, we review the analytical solutions of Landau (1+1)-dimensional hydrodynamics and exhibit the full evolution of the dynamics from the very beginning to subsequent times. Special emphasis is placed on the matching and the interplay between the Khalatnikov solution and the Riemann simple wave solution at the earliest times and in the edge regions at later times. These analytical solutions collected and developed here serve well as a useful guide and cross-check in the development of complicated numerically-intensive relativistic hydrodynamical Monte Carlo simulations.

arXiv comment11 pages, 8 figures

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• Family of New Exact Solutions for Longitudinally Expanding Ideal Fluids
• A non-boost-invariant solution of relativistic hydrodynamics in 1+3 dimensions
• Longitudinal hydrodynamics from event-by-event Landau initial conditions
• Thermal noise in non-boost-invariant dissipative hydrodynamics
• A combined model for pseudorapidity distributions in Cu-Cu collisions at BNL-RHIC energies
• Event-by-Event Study of Space-Time Dynamics in Flux-Tube Fragmentation
• A combined model for the pseudorapidity distributions in p-p collisions at center-of-mass energies from 23.6 to 7000 GeV
• Scaling behaviour of $dN/dy$ in high-energy collisions
• Landau-Khalatnikov problem in relativistic hydrodynamics
• Entropy Production in Dissipationless Hydrodynamics with an order parameter