Basing on the mass conservation equation, one can put this equation in the conservation form: ∂ ∂ ρ ρ e ∂ ∂ t + ∇ ∇ ⋅ ⋅ ( ρ ρ e u ) = 0 meaning that for an incompressible inviscid nonconductive flow a continuity equation holds for the internal energy.