We present a simplified radiation hydrodynamic model based on the fluid dynamic equations and the radiative transfer equation, which can be used to investigate the radiation properties and dynamics evolution of highly charged ions in a laser-produced plasma in vacuum. The outputs of the model consist of the evolution of the electron temperature, atom, and ion density, and the temporal and spatial evolution of various transient particles in plasma, as well as the simulated spectrum related to certain experimental conditions in a specified spectral window. In order to test the model and provide valuable experimental feedback, a series of EUV emission spectra of silicon plasmas have been measured using the spatio-temporally resolved laser produced plasma technique. The temporal and spatial evolution of the plasma is reliably reconstructed by using this model.