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Non-local, time-dependent convection models have been used to explain thelocation of double-mode pulsations in Cepheids in the HR diagram as well as theexistence and location of the red edge of the instability strip. Theseproperties are highly sensitive to model parameters. We use 2D radiationhydrodynamical simulations with realistic microphysics and greyradiative-transfer to model a short period Cepheid. The simulations show thatthe strength of the convection zone varies significantly over the pulsationperiod and exhibits a phase shift relative to the variations in radius. Weevaluate the convective flux and the work integral as predicted by the mostcommon convection models. It turns out that over one pulsation cycle the modelparameter $\alpha_{\rm c}$, has to be varied by up to a factor of beyond 2 tomatch the convective flux obtained from the simulations. To bring convectivefluxes integrated over the He II convection zone and the overshoot zone belowinto 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 andovershoot zone by radially symmetric and fluctuating quantities. Tosuccessfully model this scenario by a static, one dimensional or even by asimple time-dependent model appears extremely challenging. We conclude thatsignificant improvements are needed to make predictions based on 1D models morerobust and to improve the reliability of conclusions on theconvection-pulsation coupling drawn from them. Multidimensional simulations canprovide guidelines for developing descriptions of convection then applied intraditional 1D modelling.

Multidimensional realistic modelling of Cepheid-like variables-II: Analysis of a Cepheid model