Aiming at modeling the cavitation bubble cluster, we propose a novel nonlinear dynamic cavitation model (NDCM) considering the second derivative term in Rayleigh-Plesset equation through strict mathematical derivation. There are two improvements of the new model: i) the empirical coefficients are eliminated by introduction of the nonuniform potential functions of $\psi_v$ and $\psi_c$ for growth and collapse processes respectively, and ii) only two model parameters are required, which both base on physical quantities – the Blake critical radius $R_b$ and the average maximum growth radius $R_m.$ The corresponding cavitation solver was developed by using OpenFOAM in which we implemented the modified momentum interpolation (MMI) method to ensure that the calculated results are independent of time step size. Three validation cases, namely numerical bubble cluster collapse, ultrasonic horn experiment, and hydrodynamic cavitation around slender body are employed. The results indicate that $\psi_v$ and $\psi_c$ can reveal the nonlinear characteristics for cavity accurately, and $R_b$ and $R_m$ can reflect the relevance between cavitation model and actual physical quantities. Moreover, it is discussed the potentiality of NDCM that is generally applied on the cavitating flow possessing with dispersed bubbly cloud.