Snapshots from the Kelvin-Helmholtz instability with low density contrast at time = 1.5. The normalized density variation Δρ/Δρ₀ = (ρ − ρ₁)/(ρ₂ − ρ₁) is shown. Top row: results with density contrast of 1.5. Bottom row: results with density contrast of 1.001. Each column corresponds to a different reduction method for the speed of sound: without the RSST (ξ = 1; panels a and d), with the PVS form (ξ = 3; panels b and e), and with the DVS form (ξ = 3; panels c and f). Details of the test problem are given in Sect. 4.5.