Heretofore, studies about the modeling and simulation of Direct Steam Generation (DSG) process in parabolic trough solar collector (PTC) system are based on the spatial control volume modeling that belongs to Eulerian method. The moving boundary model is applied for the single-phase and two-phase fluid respectively. The model and the related algorithm lack necessary generality. Moreover, when system operating conditions change dramatically, the model's numerical stability is difficult to be guaranteed. For this, based on the idea of fluid parcel-tracking (FPT) of Lagrange approach, modeling and simulating the DSG dynamic process in PTC system under once-through mode are studied in this paper. A unified formulation of the variation of fluid thermodynamic properties in the absorber is built. Then, a generalized one-dimensional distribution parameter model of fluid heated and phase-change process is established. A FPT algorithm corresponding to the model is developed, by which the transient distributions of fluid thermodynamic properties and the transient position of fluid phase-change point are obtained. Additionally, the model and algorithm are primarily verified by existing experimental results. Finally, simulation experiments are carried out for studying the transient distributions of fluid thermodynamic properties in absorber under typical input disturbances, and for displaying the disappearance and regeneration process of the superheated region and two-phase region under large direct normal irradiance (DNI) disturbance. Results show that the presented model and calculation method have good versatility and can simulate the dynamic process of the DSG system. This paper possesses practical value for real-time analysis, controller design and assessment of the DSG system.