A new relativistic hydrodynamics code for high-energy heavy-ion collisions

We construct a new Godunov type relativistic hydrodynamics code in Milne coordinates, using a Riemann solver based on the two-shock approximation which is stable under the existence of large shock waves. We check the correctness of the numerical algorithm by comparing numerical calculations and analytical solutions in various problems, such as shock tubes, expansion of matter into the vacuum, the Landau-Khalatnikov solution, and propagation of fluctuations around Bjorken flow and Gubser flow. We investigate the energy and momentum conservation property of our code in a test problem of longitudinal hydrodynamic expansion with an initial condition for high-energy heavy-ion collisions. We also discuss numerical viscosity in the test problems of expansion of matter into the vacuum and conservation properties. Furthermore, we discuss how the numerical stability is affected by the source terms of relativistic numerical hydrodynamics in Milne coordinates.