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Physical modeling with numerical simulation is very useful for researchers to understand and improve the plasma-enhanced chemical vapor deposition process for coating of diamond-like carbon (DLC) films. In this paper, we implement a fluid model including a chemical reaction mechanism for methane plasmas. Employing a finite-difference method, we solve for the low-pressure RF plasma phase in a parallel-plate reactor via the local field equilibrium approximation model, based on which the distribution of the electrons and ions along with the electric potential is obtained. The validation of our simulation is carried out by comparing the model predictions with the results from a previous particle-in-cell work. Our simulations show that the concentration of neutral species is much higher than that of charged species. CH3 is found to be the major contributing species for deposition as its concentration and boundary flux are higher than those of the other depositing species. The effects of the electrode gap, reactor pressure, and RF voltage amplitude on the species density distributions and depositing species boundary fluxes are studied. Although the deposition rate may be increased (when the number density and boundary flux of depositing species increase) by changing the operating conditions, the variation of C2H5 concentration and boundary flux requires more attention because it may affect the quality of DLC coating.