Galaxies are extremely complex astrophysical objects. In order to study the evolution of galaxies, a deep understanding of many physical processes, covering a broad range of spatial and temporal scales, is required. On the smallest scales, electromagnetic radiation and particle-particle and particle-radiation interactions determine the thermal and ionisation status of the interstellar medium (ISM). On the largest scales, galactic winds and environmental effects (interactions with neighbouring galaxies and with the intracluster medium) regulate the mass budget of the galaxy and strongly affect its metallicity. Many other key physical processes such as star formation, feedback, gas circulation and stellar dynamics operate on intermediate spatial and temporal scales.
This review paper gives a summary of ingredients, methods, results and challenges encountered in the study of the chemical and dynamical evolution of galaxies, with particular emphasis on the study of dwarf galaxies (DGs). The main focus of this review is the theoretical study of the chemo-dynamical evolution of galaxies by means of computer simulations. For a broader and more comprehensive summary of properties and physical processes in galaxies, the book "Dwarf galaxies: keys to galaxy formation and evolution" (Springer) can be consulted.
The last three decades have seen an enormous surge of activity in the study of DGs, the most numerous galaxy species in the Universe. Advanced ground-based and space-born observatories have allowed the observation of these faint objects in the local volume with incredible detail. From a theoretical perspective, the interest in the study of DGs is manifold. Their shallow potential well allows an easier venting out of freshly produced metals than in more massive galaxies. Thus, DGs are perhaps significant polluters of the intracluster and intergalactic medium (, but see ). According to the hierarchical scenario for galaxy formation, dwarf galaxy-sized objects are the building blocks to form larger galaxies. DGs do not possess very prominent spiral structures or significant shear motions, hence the study of the star formation in these objects is somewhat easier than in spiral galaxies.
Besides providing key information about the kinematics of gas in galaxies, spectroscopy allows the determination of the metallicity and of the abundance ratios of specific elements. This is a very useful information because chemical abundances provide crucial clues to the evolution of galaxies. The increasing availability of large telescopes made possible the systematic study of extragalactic H II regions and other objects in external galaxies. In this way, variations of chemical composition between different galaxies and in different positions within a single galaxy could be studied. Integral field spectroscopy in this sense is a fundamental step forward. Detailed maps of the chemical abundances within a single galaxy can be obtained. In order to understand the origin of such distributions of metals, one often has to resort to the work and models of theoreticians.
Although a few basic properties of galaxies can be understood with simple analytical and semi-analytical considerations, the enormous complexity of galactic physics can only be handled (in part) with the help of numerical simulations. This is especially true for what concerns the chemical evolution of galaxies. Simple closed-box models  can provide a first-order explanation for the global metallicity in a galaxy, but the spatial distribution of metals can not be addressed with these simplified tools. On the other hand, due to the large number of processes one has to take into account, numerical simulations make generally use of results taken from other research fields and combine them in such a way that a detailed description of the evolution of galaxies can emerge. The process of simulating galaxies is thus analogous to the process of cooking. To prepare a culinary dish, ingredients must be accurately chosen, the necessary equipment must be in place, a number of steps and operations must be performed to combine the ingredients and some times a personal touch is added and standard cookbook recipes are modified in order to obtain a special effect.
For chemo-dynamical simulators of galaxy evolution, the main ingredients are:
In this review, I will consider in some detail some of these ingredients and I will describe how they have been parametrised and implemented in numerical simulations of galaxies. Ingredients related to the chemical evolution of galaxies will be treated with particular care. In the description of these ingredients, some personal bias will be applied and higher priority will be given to the most relevant ingredients for the simulation of DGs. In particular, AGN feedback will be only very briefly mentioned.
In the process of preparing a dish, the necessary equipment (pans, pots and stove) must be in place and the quality of the equipment affects the final outcome. This is also true for the numerical simulation of galaxies, where the main equipment is a computer. More often, a cluster of computers equipped with fast processors is necessary. Besides having a fast computer, appropriate algorithms and sophisticated numerical methods must be in place in order to efficiently solve the complex equations describing the evolution of galaxies. Some of these methods will be summarised in this review, too. Again, besides a very brief survey of most widely adopted methods, specific tools required for the study of the chemo-dynamical evolution of galaxies will be described with more care.
Numerical simulations always address specific issues in the evolution of galaxies, trying to give answers to open problems or trying to provide explanations to observed properties and characteristics of galaxies or groups of galaxies. In this review I will give a summary of the state-of-the-art for what concerns some of these specific issues. In particular, I will focus on the conditions for the development of galactic winds and on the fate of heavy elements, freshly produced during an episode of star formation.
The organisation of this paper is thus quite simple: there is a Section for each ingredient: initial conditions (Sect. 2), the equations (Sect. 3), the star formation (Sect. 4), the initial mass function (Sect. 5), the chemical feedback (Sect. 6), the mechanical feedback (Sect. 7) and the environmental effects (Sect. 8). In each section, commonly adopted methodologies and recipes will be introduced and some key results of past or ongoing studies will be summarised. In Sect. 9 I will summarise some relevant results of numerical investigations of DGs concerning galactic winds and their consequences. Finally, in Sect. 10 some conclusions will be drawn.