High frequency operation of standing wave thermoacoustic heat engines is attractive for space applications due to compact size and high reliability. To expedite practical use, further improvement and optimization should be based on deep understanding and quantitative analysis. This article focuses on using computational fluid dynamics (CFD) to investigate nonlinear phenomena and processes of a 300 Hz standing wave thermoacoustic engine (SWTE). The calculated model was tested in detail, which indicated that the co-axially stacked tube model was suitable for the simulation of SWTEs. Two methods of imposing temperature gradient across the stack were studied, and the processes of mean pressure increasing, pressure wave amplification and saturation were obtained under the thermal boundary condition of applying heating power. The acoustic fields were given, and the flow vortices and their evolution in both ends of the stack and resonator were observed. Moreover, a comparison between the simulation and experiments was made, which demonstrated the validity and power of the CFD simulation for characterizing complicated nonlinear phenomenon involved in the self-excited SWTEs.