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

TL;DR

This paper reviews the analytical solutions of Landau (1+1)-dimensional hydrodynamics, illustrating the full evolution of the system and emphasizing the interplay between key solutions to aid understanding and simulation validation.

Contribution

It provides a comprehensive review and detailed analysis of Landau hydrodynamics solutions, highlighting the matching between Khalatnikov and Riemann solutions at different times.

Findings

Full evolution of Landau hydrodynamics shown

Emphasis on solution matching at early and late times

Serves as a guide for numerical simulations

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.