Simulations of Solar and Stellar Dynamos and Their Theoretical Interpretation

This is the final version. Available on open access from Springer via the DOI in this recordWe review the state of the art of three dimensional numerical simulations of solar and stellar dynamos. We summarize fundamental constraints of numerical modelling and the techniques to alleviate these restrictions. Brief summary of the relevant observations that the simulations seek to capture is given. We survey the current progress of simulations of solar convection and the resulting large-scale dynamo. We continue to studies that model the Sun at different ages and to studies of stars of different masses and evolutionary stages. Both simulations and observations indicate that rotation, measured by the Rossby number which is the ratio of rotation period and convective turnover time, is a key ingredient in setting the overall level and characteristics of magnetic activity. Finally, efforts to understand global 3D simulations in terms of mean-field dynamo theory are discussed.Deutsche Forschungsgemeinschaft (DFG)European Union Horizon 2020European Research Council (ERC)CNRS/INSUCNESObservatory OSUPSUniversité Paris-SaclayUniversité Paris CitéScience and Technology Facilities Council (STFC)NAS