Large amplitude electromagnetic waves in the megahertz range can excite ionospheric turbulence and small-scale density cavities in the ionosphere near the critical layer where the electromagnetic wave is reflected. While the electromagnetic waves have wavelengths of the order 100 meters, the electrostatic waves and nonlinear structures can have wavelengths below one meter, which makes full-scale numerical simulations challenging. A full-scale numerical scheme must resolve these two length- and timesscales, as well as the ionospheric profile which is on 100 km length-scale. To overcome severe limitations on the timestep and computational load, a non-uniform nested grid method is devised, in which the electromagnetic wave is represented on a coarser grid with a spacing of a few meters and the electrostatic waves and the evolution equations for the particles are resolved on a denser grid locally in space. Interpolation and averaging schemes are used to communicate data between the coarse and dense grids. In this manner, the computational load is decreased drastically, which makes it possible to perform full-scale simulations that cover the different time- and space-scales. We discuss the simulation method and how the simulations are used to study turbulence, stimulated electromagnetic radiation and electron acceleration and heating by ionospheric turbulence.