To describe ion transport through biological channels, we derive a new Poisson-Nernst-Planck (PNP) type model called the modified PNP_steric equations with derivative terms up to the fourth order using infinite expansion (in increasing order of derivatives) of the energy with the approximate Lennard-Jones (LJ) potential. A numerical scheme of the modified PNP_steric equations is developed to see the flow dynamics of charged particles, and the special feature of the scheme is that the numerical solutions satisfy a discrete energy law mimicking the energy law of the modified PNP_steric equations. The fourth-order derivative terms of the modified PNP_steric equations may stabilize the dynamics of the modified PNP_steric equations even though the coefficients of the second-order derivative terms are located in the symmetry breaking regime which may give multiple equilibriums of the original PNP_steric equations (with B. Eisenberg, Nonlinearity 28 (2015) 2053–2080). Our numerical results show that the energy of the modified PNP_steric equations may behave like a decreasing piecewise constant function of time. Such a model and computational method would be useful for the study of ion transport through channels. This is a joint work with Yi-Ping Lo and Chun-Hao Teng.