Multidimensional realistic modelling of Cepheid-like variables

We have extended the ANTARES code to simulate the coupling of pulsation with convection in Cepheid-like variables in an increasingly realistic way, in particular in multidimensions, 2D at this stage. Present days models of radially pulsating stars assume radial symmetry and have the pulsation-convection interaction included via model equations containing ad hoc closures and moreover parameters whose values are barely known. We intend to construct ever more realistic multidimensional models of Cepheids. In the present paper, the first of a series, we describe the basic numer-ical approach and how it is motivated by physical properties of these objects which are sometimes more, sometimes less obvious. – For the construction of appropriate models a polar grid co-moving with the mean radial velocity has been introduced to optimize radial resolution throughout the different pulsation phases. The grid is radi-ally stretched to account for the change of spatial scales due to vertical stratification and a new grid refinement scheme is introduced to resolve the upper, hydrogen ioni-sation zone where the gradient of temperature is steepest. We demonstrate that th