Compressible multiphase flows occur in various engineering situations, such as appearing in cavitation, droplet atomization, and bubbly flows.  Complex flow structures may be created due to the interference between shock waves and gas-liquid interface, especially in the case of phase change. For the accurate simulation of such flows, it is necessary that the numerical solvers have not only computational stability but also suppressed numerical dissipation errors at contact discontinuous. In this study, we propose contact-preserving and stable numerical methods based on boundary variation diminishing (BVD) principle. BVD scheme has been developed as a new Godunov-type finite volume method and shows low dissipative performance. It is demonstrated that the proposed schemes can clearly capture the dynamically created interface during the compressible cavitation flows, which has been usually smeared out by the existing methods.