Vertical profiles of the Brunt-Väisälä frequency (N_BV) averaged over the time interval t ∈ (30τ_conv, 32τ_conv) in the problem of turbulent convection and wave excitation. Each panel shows the results of simulations run using the same reconstruction scheme but different Riemann solvers. Here, we only show results from the 256³ grid to avoid cluttering the figures. The reference run (REF) is represented by a black dashed line. The black dash-dotted line is the profile of the Brunt-Väisälä frequency at t = 0, and the vertical black dotted lines represent the position of the convective boundary at the beginning and the end of the chosen averaging time interval in the reference run, y = 2.168 and y = 2.174, respectively. The percentages shown in the insets for simulations run with the HLLC and LHLLC solvers represent the amplitude of the largest undershoot in N_Bv relative to N_BV,t=0, in the spatial range y ∈ (2.15, 2.40). The amplitude of the largest undershoot in the reference run is 12%.