Resolution dependence of the minimum scale height min(H_x) of the passive scalar in the Kelvin–Helmholtz problem expressed in units of the computational cell width and shown at five points in time. Grid resolution is given by the number N_x of computational cells along the x axis. The initial Mach number is $\mathcal{M}$₀ = 10⁻² and we use PSH reconstruction and the LHLLC flux function in this series of simulations. Once the steepest gradients in X become resolved the minimum scale height starts to follow the linear scaling relations shown.