Density maps for some of the 2D KH instability tests described in Sect. 3.1. From left to right, each column shows the panels for runs having initial conditions with the same Mach number at the corresponding time t = τ_KH, as listed in Table 1. From top to bottom, different rows refer to the simulations SPH, RHO, LIQ, and LP. The last one uses the linear quartic kernel but with the signal velocity (24), whereas the first three use the expression (25) (see Table 2). The plots can be compared directly with Fig. 10 of Valcke et al. (2010).