  The Peng-Robinson equation of state (PR-EoS) has become one of the most
extensively applied equations of state in chemical engineering and petroleum
industry due to its excellent accuracy in predicting the thermodynamic
properties of a wide variety of materials, especially hydrocarbons. Although
great efforts have been made to construct efficient numerical methods for the
diffuse interface models with PR-EoS, there is still not a linear numerical
scheme that can be proved to preserve the original energy dissipation law. In
order to pursue such a numerical scheme, we propose a novel energy
factorization (EF) approach, which first factorizes an energy function into a
product of several factors and then treats the factors using their properties
to obtain the semi-implicit linear schemes. We apply the EF approach to deal
with the Helmholtz free energy density determined by PR-EoS, and then propose a
linear semi-implicit numerical scheme that inherits the original energy
dissipation law. Moreover, the proposed scheme is proved to satisfy the maximum
principle in both the time semi-discrete form and the cell-centered finite
difference fully discrete form under certain conditions. Numerical results are
presented to demonstrate the stability and efficiency of the proposed scheme.
