After an overview of general aspects of modelling the pulsation- convection interaction we present reasons why such simulations (in multidimensions) are needed but, at the same time, pose a considerable challenge. We then discuss, for several topics, what insights multidimensional simulations have either already provided or can be expected to yield in the future. We finally discuss properties of our ANTARES code. Many of these features can be expected to be characteristic of other codes which may possibly be applied to these physical questions in the foreseeable future.
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