I will describe the Adaptive Refinement Tree (ART) code for cosmological simulations. The code uses a combination of particle-mesh and shock-capturing Eulerian methods for simulating the evolution of collisionless dark matter/stars and gas components, respectively. Adaptive mesh refinement (AMR) technique is used to increase the resolution in the regions of interest. The AMR is particularly attractive for cosmology because the regions where the highest resolution is needed usually occupy only a small fraction of the computational volume and thus can be refined with relatively small number of mesh cells. I will illustrate performance of the code by representative tests and applications. Specifically, I will describe very high-resolution simulations of galaxy formation and the new clues to large-scale star formation in galaxies. I will also describe simulations of galaxy cluster simulations and detailed comparisons of simulated clusters with observations.
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