Related papers: Exact analytical solutions for ADAFs
We report here on a calculation of thermalization time-scale of the two temperature advection dominated accretion flow (ADAF) model. It is established that time required to equalize the electron and ion temperatures via electron-ion…
We obtained steady solutions to the two-dimensional Boussinesq approximation equations without mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function…
A self-similar solution for time evolution of quasi-spherical, self-gravitating accretion flows is obtained under the assumption that the generated heat by viscosity is retained in the flow. The solutions are parameterized by the ratio of…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
We obtain global solutions of radiatively inefficiently accretion flows around black holes. Whether and where convection develops in a flow are self-consistently determined with the mixing-length theory. The solutions can be divided into…
We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds from the cases where convection or reaction is not present to convection-or…
We present exact solutions of the non-linear {\sc bcre} model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slope. Our solution is constructed in terms of…
We provide the complete set of global solutions of viscous transonic flows (VTFs) around black holes and neutron stars. These solutions describe the optically thick and optically thin flows from the horizon of the black hole or from the…
Comparing hydrodynamic simulations to heavy-ion data inevitably requires the conversion of the fluid to particles. This conversion, typically done in the Cooper-Frye formalism, is ambiguous for viscous fluids. We compute self-consistent…
The analytical solution is given for a vibrating rigid core sphere, oscillating up and down without volume change, situated at the center of an elastic material spherical shell, which in turn is situated inside an infinite (possible…
The non-linear fluid dynamics of a warped accretion disc was investigated in an earlier paper by developing a theory of fully non-linear bending waves in a thin, viscous disc. That analysis is here extended to take proper account of thermal…
We present a series of analytically solvable axisymmetric flows on the torus geometry. For the single-component flows, we describe the propagation of sound waves for perfect fluids, as well as the viscous damping of shear and longitudinal…
We investigate the dynamics of clumps that coexisted with/in advection-dominated accretion flows by considering thermal conductivity. Thermal conduction can be one of the effective factors in the energy transportation of ADAFs; hence it may…
In a previous paper we have written down equations describing steady-state, optically thin, advection-dominated accretion onto a Kerr black hole (Gammie and Popham 1997, hereafter Paper I). In this paper we survey the numerical solutions to…
We study a three-dimensional rapidly rotating convection model featuring tall columnar structures, in the absence of thermal diffusion. We establish the global existence and uniqueness of weak solutions, as well as the Hadamard…
The present study examines self-similarity evolution of advection dominated accretion flow (ADAF) in the presence of a toroidal magnetic field. In this research, it was assumed that the angular momentum transport is due to viscous…
Total Flow Analysis (TFA) is a method for conducting the worst-case analysis of time sensitive networks without cyclic dependencies. In networks with cyclic dependencies, Fixed-Point TFA introduces artificial cuts, analyses the resulting…
Differentially rotating, "advection-dominated" accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time-dependent quasi-spherical accretion are solved in a simplified…
In this paper, an analytical solution of alloy solidification problem is presented. We develop a special method to obtain an exact analytical solution for mushy zone problem. The main key of this method is a requirement that thermal…
Hydrodynamics and magnetohydrodynamic simulations of hot accretion flow have indicated that there is an inward decreasing of mass accretion rate with decreasing radius. Consequently, we have a flatter density profile ($\rho \propto r^{-p}$…