Modeling and Simulation of Circumstellar Disks with the Next Generation of Hydrodynamic Solvers

This thesis is a computational study of circumstellar gas disks, with a special focus on modeling techniques and on numerical methods not only as scientific tools but also as a target of study. In particular, in-depth discussions are included on the main numerical strategy used, namely the moving-mesh method for astrophysical hydrodynamics. In this work, the moving-mesh approach is used to simulate circumstellar disks for the first time.