This workshop had been initiated by the recognition that current theoretical models for stars are no longer accurate enough to explain a multitude of astronomical observations. Examples for these are asteroseismological inferences about the internal structure of stars, spectroscopic determinations of chemical abundances at the surfaces of stars, and the consequences for the chemical evolution of whole galaxies. The shortcomings of the - so far quite successful - theory of stellar structure and evolution can be traced back to the rather superficial and approximate treatment of hydrodynamical processes in stars, which are, by their nature, multi-dimensional, while stellar models are almost exclusively computed under the assumption of hydrostatic conditions and spherical symmetry.

The Lorentz Center provided the perfect environment for 40 scientists from 10 countries to gather and discuss the challenges for stellar evolution theory, the progress made with 1-D models, the capabilities of the current generation of multi-dimensional models, and possible paths to improve the former by using the latter. During the first two days the challenges and shortcomings of the 1-D models were discussed in a very candid and constructive way.  Given that such models will also be the workhorse of stellar evolution in the foreseeable future, ways to model intrinsically multi-D processes within 1-D stellar evolution calculations were also presented. The following sessions saw the impressive efforts in the current hydrodynamical modelling of convection and rotation, as well as the limitations of such simulations. Evidently, only small parts of stars or time-limited phases can be followed in detail, and sub-resolution effects - in particular in the case of turbulence - are requiring either correct sub-scale models, or impose computational efforts still beyond supercomputer capabilities.

The workshop ended on the last day with an extensive discussion about strategies to improve stellar models. Indeed, thanks to the stimulating environment of the Lorentz Center and the various shorter discussion sessions that took place during the preceding days, a number of possibilities were suggested.  They range from detailed verifications of simplified physics using asteroseismological objects, to joint efforts of various groups performing multi-D simulations (e.g. for code and numerical method verification), to the idea of designing a "Grand Challenge" simulation, in which several of the groups represented in the workshop apply jointly for substantial amounts of computing time at one of the forefront supercomputer centres. Also, a number of working and discussion groups were established, some of them considering to apply for future workshops at Snellius. The participants also favoured a follow-up workshop within the next few years to keep up the momentum gathered during this very satisfying week.

The organizers feel that the purpose of the workshop has been reached and even exceeded: various research fields were brought together, the needs of the 1-D community and the possibilities of multi-D simulations were presented, the regions of productive overlap defined, and the wealth of high-quality, new observational results has been acknowledged to provide invaluable input for the further development of stellar models.

The organizers thank the Lorentz Center for providing the ideal environment for this workshop, and its staff for the efficient coordination and the pleasant and friendly cooperation. Financial support by the Max-Planck-Institute for Astrophysics (Garching), NOVA, and NWO is gratefully acknowledged.



Onno Pols (Nijmegen, The Netherlands)

Maurizio Salaris (Liverpool, United Kingdom)

Henk Spruit (Garching, Germany, and Amsterdam, The Netherlands)

Achim Weiss (Garching, Germany)