Galaxy formation and evolution is one of the most challenging tasks in astrophysics.There is strongly increasing and substantial progress in this field not only due to theincrease of telescope size and developments of new techniques providing observationsallover the electromagnetic spectrum, but also the development of advanced computerarchitectures and of sophisticated numerical codes allow to tackle this problem from bothsides and to link both research approaches to a fruitful progress in astrophysics. Thisreview will not focus on the application of a single numerical method and the descriptionof its result, but is instead aiming at providing an overview of different numerical toolson the basis of particle and grid schemes and to referring to important publications forthe intersted reader.

In this brief review I sum up some recent progress in the area of stellar dynamics,focusing on the dynamics of self-bound stellar associations in isolation and in(approximate) equilibrium. The basics of stellar dynamics are first outlined and theimportance of stellar evolution is stressed. Subsequently I argue that the evolution ofmulti-mass clusters in the point-mass approximation still holds clues to the dynamics ofgalaxy nuclei. I take a more personal standpoint when discussing the role of stellarevolution on the dynamics over relaxation time scales and draw from several recent modelsto underscore that a major step forward has been made in the coupling of stellar evolutionand dynamics. I then briefly visit the issue of multiple stars and highlight some as yetunsolved problems.

Observing nearby interacting galaxies is a key to understanding galactic physics providedthat we know the spatial and temporal perturbations acting on these galaxies. Thus, wehave to know the orbits and the gross internal properties of the galaxies. In order tocope with the related extended parameter space, we developed the code MINGA whichcombines a genetic algorithm with a fast N-body method. As an example for this method, wepresent a re-analysis of the prototypical system NGC 4449 which is now based on both, thefull HI data cube of the NGC 4449 system and on improved determinations of the galacticorbits within a restricted N-body calculation.

Motivated by the closest major merger, the Antennae Galaxies (NGC4038/4039), we want toimprove our genetic algorithm based modeling code Minga (Theis 1999). The aim is to reveal the major interaction andgalaxy parameters, e.g. orbital information and halo properties of suchan equal mass merger system. Together with the sophisticated search strategy ofMinga, one needs fast and reliable models in order to investigate the highdimensional parameter space of this problem. Therefore we use a restrictedN-body code which is based on the approach by Toomre & Toomre(1972), however with some refinements likeconsistent orbits of extended dark matter halos. Recently also dynamical friction wasincluded to this code (Petsch 2007). While a gooddescription for dynamical friction was found for mass ratios up toq = 1/3 (Petsch & Theis 2008), major merger systems were only imperfectly remodeled. Here we show recentimprovements for a major merger system by including mass-loss and using NFW halos.

We describe some results obtained with N-MODY, a code for N-bodysimulations of collisionless stellar systems in modified Newtonian dynamics (MOND). Wefound that a few fundamental dynamical processes are profoundly different in MOND and inNewtonian gravity with dark matter. In particular, violent relaxation, phase mixing andgalaxy merging take significantly longer in MOND than in Newtonian gravity, whiledynamical friction is more effective in a MOND system than in an equivalent Newtoniansystem with dark matter.

We aim to study of the formation and evolution of galaxies with high spatial and temporalresolution. We describe a new chemodynamical code to describe the physical interplaybetween the stars and the multiphase interstellar medium in galaxies, including a dustcomponent. Preliminary results can be found in Champavert (2007).

We study the proximity effect around high redshift quasars in dependence on the quasarredshift and environment using 3D continuum radiative transfer simulations. Snapshots ofdark matter only simulations at redshift 3, 4, and 4.9 are mapped to hydrogen densitiesand temperatures using an effective equation of state. The overionization zone around QSOswith luminositiesLνHI = 1031and1032   ergHz-1s-1is studied in a UV background field in radiation equilibrium. By analyzing syntheticspectra of lines of sight originating at the QSO, the proximity effect is studied. We findthat the quasar spectral energy distribution, diffusion and shadowing due to Lyman Limitsystems play a role in the signal. Density inhomogeneities around the QSO are responsiblefor a large scatter around the mean proximity effect seen in all simulated QSO spectra.This scatter is larger than the differences arising from varying quasar hostenvironments.

We performed cosmological simulations based upon both a cold dark matter (CDM) and a warmdark matter (WDM) model. The focus of our investigations lies with selected spatial andkinematic properties of substructure halos (subhalos) orbiting withinhost halos, that form in both dark-matter cosmologies. We aim at using the dynamics of thesubhalos as a probe of the respective cosmology.

Using a set of high-resolution dark matter only cosmological simulations we found acorrelation between the dark matter halo mass M and its spin parameterλ for objects forming at redshifts z > 10: thespin parameter decreases with increasing mass. However, halos forming at later times donot exhibit such a strong correlation, in agreement with the findings of previous studies.

While we presented such a correlation in a previous study using the Bullock etal. (2001) spin parameter defintion wenow defer to the classical definition showing that the results are independent of thedefinition.

We present a novel solver for an analogue to Poisson’s equation in the framework ofmodified Newtonian dynamics (MOND). This equation is highly non-linear and hence standardcodes based upon tree structures and/or FFT’s in general are not applicable; one needs todefer to multi-grid relaxation techniques. We present results from the first cosmologicalsimulations we made to compare cosmological structure formation of in the two paradigms.We found compatible results between the two simulations, at least at redshiftz = 0.

Hot, underdense bubbles powered by active galactic nuclei (AGN) are likely to play a keyrole in halting catastrophic cooling in the centers of cool-core galaxy clusters. Wepresent three-dimensional simulations that capture the evolution of such bubbles, using anadaptive-mesh hydrodynamic code, FLASH3, to which we have added a subgrid model ofturbulence and mixing. Pure-hydro simulations indicate that AGN bubbles are disrupted intoresolution-dependent pockets of underdense gas. However, proper modeling of subgridturbulence shows that Rayleigh-Taylor instabilities act to mix the heated regions withtheir surroundings, while at the same time preserving them as coherent structures,consistent with observations. Thus bubbles are transformed into hot clouds of mixedmaterial as they move outwards in the hydrostatic intracluster medium. Properly capturingthe evolution of such clouds has important implications for many ICM properties.

Recently, the MID-infrared Interferometric instrument (MIDI) at the VLTI has shown thatdust tori in the two nearby Seyfert galaxies NGC 1068 and the Circinus galaxy aregeometrically thick and can be well described by a thin, warm central disk, surrounded bya colder and fluffy torus component. By carrying out hydrodynamical simulations with thehelp of the TRAMP code (Klahr et al. 1999), we follow the evolution of a young nuclear star cluster in terms ofdiscrete mass-loss and energy injection from stellar processes. This naturally leads to afilamentary large scale torus component, where cold gas is able to flow radially inwards.The filaments join into a dense and very turbulent disk structure. In a post-processingstep, we calculate spectral energy distributions and images with the 3D radiative transfercode MC3D Wolf (2003) and compare them toobservations. Turbulence in the dense disk component is investigated in a separateproject.

Supernovae are known to be the dominant energy source for driving turbulence in theinterstellar medium. Yet, their effect on magnetic field amplification in spiral galaxiesis still poorly understood. Analytical models based on the uncorrelated-ensemble approachpredicted that any created field will be expelled from the disk before a significantamplification can occur. By means of direct simulations of supernova-driven turbulence, wedemonstrate that this is not the case. Accounting for vertical stratification and galacticdifferential rotation, we find an exponential amplification of the mean field ontimescales of 100 Myr. We highlight the importance of rotation in the generation ofhelicity by showing that a similar mechanism based on Cartesian shear does not lead to asustained amplification of the mean magnetic field.

We present a numerical study on the behavior of the density power spectrum resulting fromcompressible hydrodynamic, thermally unstable simulations with different rms Mach numbersMrms. We find that the spectrum becomes shallower asM increases and that spectral index values that are consistent withthose reported from observations.

Stars can be seen as modern physics laboratory from which fundamental processes asdiverse as atomic physics or turbulence can be studied and understood. Being able to modelaccurately their structure, dynamic and evolution is thus of fundamental importance and isthe subject of intense research. In this short review we will present some of thenumerical simulations in three dimensions performed in recent years to model such complexand nonlinear objects, focussing mostly our discussion on results obtained with theanelastic spherical harmonic (ASH) code. Using the Sun as a reference star, we wish togain insight and to constrain magnetohydrodynamical processes (such as Reynolds andMaxwell stresses, meridional circulations, differential rotation (i.e. ω-effect), thermal wind, α-effect) at theorigin of the solar small and large scale dynamics and magnetism. We will then extend ourstudy to other stars, such as young Suns, massive stars or evolved RGB stars in order toidentify which processes are at the origin of their significantly different dynamics.

The ANTARES code (A Numerical Tool for Astrophysical RESearch) is designed for doing 1D,2D and 3D stellar (radiation-, magneto-) hydrodynamics with realistic microphysics,applying various high-resolution numerical schemes, optionally local grid refinement andworks with rectilinear or spherical coordinates.– We present results on turbulent solargranulation flows which have been done in 2D and 3D and comment on our simulations of thepulsation-convection interaction in Cepheid variables, presently 2D.

Our paper intends to estimate the EUV dimming appearing in a prominence eruption into acoronal mass ejection from the observationally point of few and so well from a numericalmodel. We have performed a numerical MHD simulation on a solar radius and obtained a CMEoriginating from a prominence. The mass dimming was revealed clearly and we compared themass evolution of the CME to that of an event observed on 14 January 2001 by SOHO.

To explain important properties of extrasolar planetary systems (e.g.close-in hot Jupiters, resonant planets) an evolutionary scenario which allowsfor radial migration of planets in disks is required. During their formation protoplanetsundergo a phase in which they are embedded in the disk and interact gravitationally withit. This planet-disk interaction results in torques (through gravitational forces) actingon the planet that will change its angular momentum and result in a radial migration ofthe planet through the disk. To determine the outcome of this very important process forplanet formation, dedicated high resolution numerical modeling is required. Thiscontribution focusses on some important aspects of the numerical approach that we foundessential for obtaining successful results. We specifically mention the treatment ofCoriolis forces, Cartesian grids, and the FARGO method.

We investigate the influence of radiative transport on the growth of themagnetorotational instability (MRI) in accretion discs. A general dispersion relationdescribing the growth of small disturbances on a homogeneous background shear flow isprovided. It includes compressibility and radiative effects in the flux-limited diffusionapproximation. All the effects of radiation transport can be subsumed into one singleparameter, an effective speed of sound. Radiative diffusion does not affect the regionwhere the MRI operates, but it alters the growth rates of the MRI either by increasing ordecreasing them. We report about corresponding numerical simulations, which are also usedfor a first investigation of the non-linear stage of the MRI in gas-pressure dominatedaccretion discs with radiation transport included.