Evolution of the internal energy of the disc normalised with respect to the initial internal energy of the disc and relative to the 2D simulations of a recoiling black hole. Different lines refer to simulations with uniform grid using three different resolutions: 256 × 128 (red solid line), 512 × 256 (green solid line), and 1024 × 512 (blue solid line). We also show the internal energy for AMR simulations using three levels with different tolerances of ε_t = 0.1 (blue dashed) and ε_t = 0.005 (blue dash-dotted).