Comparison between 1D and 2D numerical solutions of the RHD wave. Top panel: density perturbation profile of an RHD wave after 40 oscillation periods. In black, the analytically predicted profile, in blue results from a 1D simulation and in red results from a 2D simulation with the wave vector parallel to the first diagonal. The x-axis is here chosen in the direction of the wave vector. Bottom panel: respective residuals calculated as |ρ − ρ_analytic|/ρ_analytic, where the analytic density is calculated from perturbation theory.