The University of Alaska Fairbanks Eulerian Polar Parallel Ionospheric Model is a high-resolution model of the polar ionosphere that incorporates multiple ion species. This paper briefly describes this model and the implementation of the total variation diminishing (TVD) advection scheme. The model is based on an Eulerian framework. It is demonstrated that the minimal numerical diffusion of the TVD advection scheme is critical for maintaining ion density gradients with high-resolution Eulerian ionospheric models. The performance of this method is discussed and compared with an upwind numerical scheme. A sample model run for 24 October 2003 that simulates the formation of polar cap ionospheric structures is presented. The results using the TVD advection scheme are compared with the corner transport upwind advection scheme to demonstrate the advantage of the TVD method for simulating steep density gradients and small-scale density structures. These small-scale density features result from time-varying electric fields and are commonly observed using experimental techniques (e.g., incoherent scatter radar) in polar regions.