Here, the fully implicit and scalar ADI type implicit preconditioning formulations based on the Riemann solvers for multi-phase flows are performed. The numerical stability problem caused by the multi-scale speed of sound due to uncertain dissipation terms in the current schemes that can be resolved by rescaling the eigenvalues of the Euler type system equations to enhance computational convergence. This paper presents implicit pre-conditioning approaches which indicate similarly accurate results obtained with both schemes. The current used homogeneous two-phase mixture model with the assumption of kinematics and thermodynamics equilibriums. The thermodynamics behaviors of liquid phase, vapor phase and their phase transitional process are described by a temperature dependent hybrid equation of state which includes a mass-fraction averaged formula of water-vapor saturation process. The current work shows that the implicit schemes are capable of improving the computational efficiency over its explicit counterpart. Several benchmark tests are used for numerical validations.
