Energies and total energy conservation as a function of time from the standard (left) and well-balanced (right) scheme with N = 512. In both panels, the solid (blue) line is the internal energy E_int, the dashed (green) line is the kinetic energy E_kin, the dash-dotted (red) line is minus the gravitational energy −E_grav and the dotted (black) line is the total energy conservation ΔE.