Non-local, time-dependent convection models have been used to explain the location of double-mode pulsations in Cepheids in the HR diagram as well as the existence and location of the red edge of the instability strip. These properties are highly sensitive to model parameters. We use 2D radiation hydrodynamical simulations with realistic microphysics and grey radiative-transfer to model a short period Cepheid. The simulations show that the strength of the convection zone varies significantly over the pulsation period and exhibits a phase shift relative to the variations in radius. We evaluate the convective flux and the work integral as predicted by the most common convection models. It turns out that over one pulsation cycle the model parameter $alpha_{rm c}$, has to be varied by up to a factor of beyond 2 to match the convective flux obtained from the simulations. To bring convective fluxes integrated over the He II convection zone and the overshoot zone below into agreement, this parameter has to be varied by a factor of up to $sim 7.5$ (Kuhfu{ss}). We then present results on the energetics of the convection and overshoot zone by radially symmetric and fluctuating quantities. To successfully model this scenario by a static, one dimensional or even by a simple time-dependent model appears extremely challenging. We conclude that significant improvements are needed to make predictions based on 1D models more robust and to improve the reliability of conclusions on the convection-pulsation coupling drawn from them. Multidimensional simulations can provide guidelines for developing descriptions of convection then applied in traditional 1D modelling.
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