Preface

The process by which a massive compact object (like white dwarfs, neutron stars, black holes etc) gravitationally captures ambient matter is called accretion. The accretion of matter on to a compact massive star is the likely source of energy in the observed binary X-ray sources. Since black holes are ‘black’, there cannot be any direct observational evidence of them. Thus they must be observed by detecting the radiations emitted by accreting matter. For typical gas dynamical conditions found in the interstellar medium and in the matter exchanged between the binary stars, it is expected that accretion flows on to compact objects will be hydrodynamical or magneto-hydrodynamical in nature. Thus, to study black hole accretion, it is necessary to know the hydrodynamic properties of the flow of the matter as it is the matter which, after all, will emit the radiation that we detect by satellites. The variation of thermodynamic quantities such as the initial energy density of the accreted matter plays important roles as the emitted radiation intensity from the flow depends on the density and the temperature at each point of the flow at each moment of time. So the spectral and temporal properties of emitted radiations are directly determined by the hydrodynamical variables. In my Ph.D. work, I mainly made effort to study the hydrodynamic properties of the flow and its stability properties through time-dependent numerical simulations. We started with time-dependent solutions of one-dimensional (spherically symmetric) and two-dimensional (axially symmetric) accretion flows around compact objects, in particular black holes, after examining the steady-state solutions. We describe the development of a two-dimensional hydrodynamic code and its application to various astrophysical problems. A FORTRAN code for two-dimensional numerical hydrodynamics has been developed to model viscous accretion discs. We employ a grid-based finite difference method called the total variation diminishing method (TVD). The effective shear viscosity present in the code is evaluated. The simulations were carried out for flows in the Schwarzschild geometry. By numerical simulation, we show that the theoretical solutions (with or without shocks) which are claimed to be stationary are indeed so. When the shocks are absent, they show steady oscillations. Our survey was carried out using the entire inflow parameter space spanned by the specific energy, angular momentum, shear viscosity and a