The non-linear dynamics of cosmological perturbations of an irrotational collisionless fluid is analyzed within General Relativity. Relativistic and Newtonian solutions are compared, stressing the different role of boundary conditions in the two theories. Cosmological implications of relativistic effects, already present at second order in perturbation theory, are studied and the dynamical role of the magnetic part of the Weyl tensor is elucidated.

No abstract

No abstract

Numerical simulations of galaxy clusters including two species -baryonic gas and dark matter particles -are presented. Cold Dark Matter spectrum, Gaussian statistics and flat universe are assumed. The dark matter component is evolved numerically by means of a standard particle mesh method. The evolution of the baryonic component has been studied numerically by using a multidimensional (3D) hydrodynamical code based on modern high resolution shock capturing techniques. These techniques are specially designed for treating accurately complex flows in which shocks appear and interact. With this picture, the role of shock waves in the formation and evolution of rich galaxy clusters is analyzed. Our results display two well differenced morphologies of the shocked baryonic matter: filamentary at early epochs and quasi-spherical at low redshifts.Subject headings: cosmology: theory-hydrodynamics-large-scale structure of the universe -methods:numerical-shock waves SPH methods were first proposed by Gingold &Monaghan (1977), and Lucy (1977).Among the best features of this technique, it should be pointed out its high resolution in dense regions. This property is directly derived from its Lagrangian character. The first implementations of SPH techniques had some weak points: i) The low density regions were badly described due to the Lagrangian character of the method. ii) Discontinuities and strong gradients were poorly solved and an important diffusion was introduced. iii) They were not conservative. Nevertheless, these previous problems were overcome in the modern implementations of these techniques. Improved SPH techniques have been widely developed for cosmological applications (see, e.g.Numerical cosmological codes using an Eulerian approach to study baryonic gas inside galaxy clusters have been also developed. Some of these hydro-codes use artificial viscosity in order to deal with shock waves (Cen 1992, Anninos et al. 1994. These techniques require a good calibration of the free parameters which are introduced by hand and state some numerical problems. Recently, a new family of finite difference methods, which use Eulerian approaches and avoid artificial viscosity, has been developed in numerical Cosmology. They are the so-called high resolution shock capturing methods (HRSC), the modern extensions of the original Godunov's idea (1959). According to the Riemann solver and the procedure in order to achieve spatial accuracy, we can distinguish three groups: 1) the ones following Harten's scheme (1983), like Ryu et al. (1993), 2) those using the analytical solution of the Riemann problem for the Newtonian dynamics of ideal gases and the PPM scheme described by Collela & Woodward (1984) , like Bryan et al. (1994), and 3) the codes using Roe's Riemann solver (Roe 1981) plus the MUSCL or PPM cell reconstruction, like inQuilis et al. (1996). In this last reference, the code used in present paper is described and tested appropriately.