In order to tackle the issues of poor mobility and unstable traction of electric vehicles on sandy landscapes, this research develops a high-accuracy numerical model for wheel-sand interaction relying on the Discrete Element Method (DEM). An innovative parameter calibration procedure is proposed herein, which optimizes the sand contact parameters. This reduces the error between the simulated and measured angles of repose to merely 1.2% and substantially improves the model's reliability. The model was then used to systematically compare the performance of a 205/55 R16 slick tire with a treaded tire on sand. Simulations demonstrate that at a 30% slip ratio, the treaded tire exhibited significantly higher traction and greater sinkage than the slick tire. This indicates that tread patterns enhance traction mechanically by increasing the contact area and promoting shear deformation of the sand. The trends of traction with slip ratio and the corresponding sand flow patterns showed excellent agreement with experimental observations, which validated the simulation approach. This research provides an efficient and accurate tool for evaluating tire-sand interaction, providing critical support for the design and control of electric vehicles on complex terrains.