| 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.;The structure of the thesis follows a natural progression that begins by discussing the role of computational methods in modern astrophysics, followed by a description of the moving-mesh method as a general solver for gas dynamical problems, and concluding with detailed modeling of circumstellar disks in two and three dimensions, both in isolation and in pairs.;The thesis structure consists of two parts. Part I --second and third chapters-- focuses on moving-mesh hydrodynamics and Voronoi meshes in general, deriving the discretized equations of the method from first principles and describing the time-stepping technique in detail. This section also includes original work on numerical methods to include diffusion terms to the equations of hydrodynamics, such as physical viscosity.;In Part II of the thesis --fourth, fifth and sixth chapters-- the attention is turned to circumstellar disks. In the fourth chapter, two-dimensional disk simulations are carried out as a benchmarking stage, before more complex, three-dimensional models can be pursued. Novel techniques for creating stable, three-dimensional models of self-gravitating disks with finite radius are discussed in the fifth chapter. In this model, the Voronoi discretization of the computational domain allows for a smooth transition between the mesh that discretizes the disk and the mesh that discretized the background space. Details are provided on how stationary models can be created a priori without the need for relaxation procedures as done in previous work.;Finally, the sixth chapter includes a set of simulations that, owing to their complexity, require a scheme that combines the features of the method discussed in preceding chapter. Specifically, such a scheme must be capable of treating self-gravitating systems that (1) lack an obvious symmetry, (2) include regions of high-Mach number flow, (3) have a large dynamical range in density and (4) need an adaptive mesh resolution to adequately capture strongly compressed/shocked regions and potentially fragmentation. To this end, a suite of novel simulations of disk-disk interaction is carried out, to conduct an initial study of the tidal effects that massive disks have on the evolution of their host stars' orbits. |
