Assessment of the gray M₁ model in the case of a laboratory radiative shock simulation

The paper deals with the issue of assessing approximate models used for the treatment of radiation coupled with hydrodynamics equations. Radiation plays a key role in many astrophysical structures, such as accretion shocks on classical T Tauri stars, but also in experimental flows, such as plasmas generated in laser driven radiative shocks. It is therefore crucial to test the accuracy of the approximate radiation moment models used in radiation hydrodynamics (RHD) calculations. Based on a laboratory shock simulation test case, we present comparisons of approximate radiation quantities calculated with the gray M₁ model with the three-dimensional (3D) RHD code HERACLES, and reference radiation quantities obtained after solving the radiative transfer equation with the 3D radiative transfer code IRIS by post-processing a HERACLES structure. Our results indicate that radiation quantities are correctly calculated by M₁ in regions of the computational domain far from lateral boundaries, from which photons can freely escape, and through which no photon can enter from the outside. However, M₁ fails to reproduce correct quantities in the vicinity of these boundaries. We suggest to implement an improved version of the M₁ model: a half-moment model that makes it possible to distinguish between incoming flux and outgoing flux at boundaries.