{ ρ ρ m , n + 1 = ρ ρ m , n − − 1 V m ∫ ∫ t n t n + 1 ∮ ∮ ∂ ∂ V m ρ ρ u ⋅ ⋅ n ^ ^ d s d t u m , n + 1 = u m , n − − 1 ρ ρ m , n V m ∫ ∫ t n t n + 1 ∮ ∮ ∂ ∂ V m ( ρ ρ u ⊗ ⊗ u − − p I ) ⋅ ⋅ n ^ ^ d s d t e m , n + 1 = e m , n − − 1 2 ( u m , n + 1 2 − − u m , n 2 ) − − 1 ρ ρ m , n V m ∫ ∫ t n t n + 1 ∮ ∮ ∂ ∂ V m ( ρ ρ e + 1 2 ρ ρ u 2 + p ) u ⋅ ⋅ n ^ ^ d s d t .