We present initial results from three-dimensional (3-D) radiation hydrodynamical simulations for the Sun and targeted Sun-like stars. We plan to extend these simulations up to several stellar days to study p-mode excitation and damping processes. The level of variation of irradiance on the time scales spanned by our 3-D simulations will be studied too. Here we show results from a first analysis of the computational data we produced so far.

A lot of effort has been devoted to the hydrodynamical modelling of Cepheids in one dimension. While the recovery of the most basic properties such as the pulsational instability itself has been achieved already a long time ago, properties such as the observed double-mode pulsation of some objects and the red-edge of the classical instability strip and their dependence on metallicity have remained a delicate issue. The uncertainty introduced by adjustable parameters and further physical approximations introduced in one-dimensional model equations motivate an investigation based on numerical simulations which use the full hydrodynamical equations. In this talk, results from such two-dimensional numerical simulations of a short period Cepheid are presented. The importance of a carefully designed numerical setup, in particular of sufficient resolution and domain extent, is discussed. The problematic issue of how to reliably choose fixed parameters for the one-dimensional model is illustrated. Results from an analysis of the interaction of pulsation with convection are shown concerning the large-scale structure of the He ii ionization zone. We also address the influence of convection on the atmospheric structure. Considering the potential of hydrodynamical simulations and the wealth of ever improving observational data an outlook on possible future work in this field of research is given.

Numerical simulations of convection near the solar surface are now advanced enough to reproduce both a large set of observational data and provide tests for convection models. We discuss the role of coherent structures in models of solar p-mode excitation, for which the analysis of numerical simulations has provided key inputs in the modelling. The robustness of these simulations is shown by a comparison illustrating the influence of boundary conditions on ensemble averaged quantities. In a concluding example advanced high resolution simulations are shown to resolve the onset of shear driven turbulence generated by up- and downflow structures.

We discuss how 3D numerical simulations can be used to analyse the different contributions within dynamical equations of non-local Reynolds stress models of convection.

A summary of the round table discussion following Session A on Modelling Convection and Radiative Transfer is provided based on the video recording made during the conference.

We use numerical simulations of granulation in the Sun and a K dwarf to study the effects of coherent structures on higher order moments. The latter need to be calculated in non-local Reynolds stress models of turbulent convection. Models that explicitly account for the asymmetry between up- and downflows as well as hot and cold drafts provide a substantial improvement over traditional ones, such as the quasi-normal approximation, which is only able to provide order of magnitude estimates for this type of flow.

Oscillations of stellar p modes excited by turbulent convection are investigated. In the uppermost part of the solar convection zone, radiative cooling is responsible for the formation of turbulent plumes, hence the medium is characterized with downdrafts and updrafts. The motivation is to take the asymmetry of up- and downflows created by turbulent plumes into account through an adapted closure model. We built a generalized two-scale mass-flux model (GTFM) that considers both the skew introduced by the presence of two flows and the effect of turbulence onto each flow. In order to apply the GTFM to the solar case, we introduce the plume dynamics as modelled by Rieutord & Zahn (1995) and construct a closure model with plumes (CMP). The CMP enables to express third- and fourth-order velocity correlation products in terms of the second-order ones. When comparing with 3D numerical simulation results, the CMP improves the agreement for the fourth order moments in comparison with the quasi-normal approximation (QNA) or the classical mass-flux model (MFM). This excitation model reproduces the maximum of the power supplied to solar p modes, when compared with GOLF observations.

We discuss some benefits and pitfalls when combining conceptually different types of closure approximations into complete Reynolds stress models of stellar convection.

We introduce an extended 3D numerical simulation study of Reynolds stress models of stellar convection and probe fluxes as well as mean temperature gradient profiles.

Excitation of solar-like oscillations is attributed to turbulent convection and takes place at the upper-most part of the outer convective zones. Amplitudes of these oscillations depend on the efficiency of the excitation processes as well as on the properties of turbulent convection. We present past and recent improvements on the modeling of those processes. We show how the mode amplitudes and mode line-widths can bring information about the turbulence in the specific cases of the Sun and α Cen A.

We provide results from an extended numerical simulation study of Reynolds stress models of stellar convection and probe the modelling of third order moments and non-locality.

We present the essential features of the ANTARES code. ANTARES has been developed to perform the simulation of astrophysical flows in one, two, or three dimensions. Using, in particular, the option of grid refinement, we present results for solar granulation achieved at very high spatial resolution.

Microturbulence is usually treated in model atmospheres as a free parameter (ξt) that allows to re-establish agreement among abundances derived from different lines. Even if this parameter is a consequence of treating a 3D problem as a 1D one, it seems clear that microturbulence is linked to the velocity field within the atmosphere, and therefore to convection in the external layers. The values of the parameter as determined from observations show a dependence both on effective temperature and on surface gravity. In this paper we study how the microturbulence parameter used in the atmosphere models affects the theoretical color-magnitude diagram (CMD). First, in the Main Sequence (MS) domain due to the dependence of the microturbulence parameter on Teff; and second, in the giant branch (Pre-main sequence and Red Giant Branch) where several photometric indexes show a large variation due to the increase of the microturbulence parameter as the stellar gravity decreases. We predict then a significant change in the CMD, as well as in the color-temperature calibrations, if variations of ξt such as those observationally determined are included in theoretical CMD computations.

We provide results from an extended 3D numerical simulation study of Reynolds stress models of stellar convection and probe the modelling of compressibility, pressure fluctuations, and dissipation of turbulent kinetic energy.

Narrow band photometry is a useful tool to characterize large numbers of stars, but observed colors and indices must be connected to astrophysical parameters by synthetic photometry. We present synthetic Hβ indices calculated from 1D model atmospheres implementing different convection treatments. The calculated indices are transformed to the standard system using observed medium-resolution spectra. We test the synthetic photometry with observed indices of eclipsing binary systems. The computed indices agree with the observed ones up to an amount expected from the observational errors, the accuracy of the atmospheric parameters, and computational uncertainties.

The spectra of a number of reportedly sharp-line B, A and F stars havebeen observed in a 60-Å window with a resolving power of 120 000.As a first step in analysis of these data, the spectra have beensynthesized to see how well simple models fit. The informationobtained from both successful modelling and from discrepant fits isdiscussed.