Numerical technique is developed to clean spurious magnetic field divergence ▽·B in full MHD (Magnetohydrodynamics) simulation.Eight-wave equations are solved in basic scheme combined with additional source term ▽·B to keep conservation.A projection scheme is used to clean spurious magnetic field divergence.3D Poisson equation is solved with a finite volume method.For smooth analytical field,▽·B is cleaned efficiently.While for hypersonic MHD blunt flows with shock wave,▽·B error increases sharply in free stream region.A local projection scheme is proposed to clean ▽·B in relatively high divergence region. Flow field converges well and magnetic field divergence in low divergence region is not influenced.