We performed two-dimensional smoothed particle hydrodynamics (SPH) simulations of SU UMa stars during superoutburst using the parameters of four systems with well-known orbital and superhump periods. We establish that only in systems with mass ratios q=M_1/M_2>~4 do eccentric accretion discs evolve. This is in excellent agreement with theory. The simulated light curves show superhumps with the same period and amplitude as the observations. The observed temporal development of the superhumps is also reproduced in the simulations: the period diminishes slightly and secondary structures evolve during the superoutburst. The superhump period is found to depend on the viscosity parameter and the mass-transfer rate. The amplitude of the shifts in the gamma-velocity is in accordance with observations and their period can be identified as the beat period between the superhump and the orbital period. In the SPH code a physical viscosity is implemented, instead of the common artificial viscosity. Our results confirm the combined tidal and thermal instability model for superoutbursts by Whitehurst, as well as the model for gamma-shifts by Vogt.