What are the governing equations used in CFD?

CFD solves three fundamental conservation equations: (1) Continuity equation (mass conservation): ∂ρ/∂t + ∇·(ρV) = 0. (2) Momentum equations (Navier-Stokes): ρDV/Dt = -∇P + μ∇²V + ρg, representing Newton's second law for fluids with pressure, viscous, and body forces. (3) Energy equation: ρD(e)/Dt = -P(∇·V) + ∇·(k∇T) + Φ, where Φ is viscous dissipation. These partial differential equations are discretized using finite difference, finite volume, or finite element methods and solved iteratively. Additional equations are needed for turbulence (RANS, LES) and multiphase flows.