If one expands the material derivative the equations above are: { ∂ ∂ ρ ρ ∂ ∂ t + u ⋅ ⋅ ∇ ∇ ρ ρ + ρ ρ ∇ ∇ ⋅ ⋅ u = 0 ∂ ∂ u ∂ ∂ t + u ⋅ ⋅ ∇ ∇ u + ∇ ∇ p ρ ρ = g ∂ ∂ e ∂ ∂ t + u ⋅ ⋅ ∇ ∇ e + p ρ ρ ∇ ∇ ⋅ ⋅ u = 0