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We study the effects of initial and boundary conditions, takingtwo-dimensional hydrodynamical numerical simulations of hot accretion flow asan example. The initial conditions considered include a rotating torus, asolution expanded from the one-dimensional global solution of hot accretionflows, injected gas with various angular momentum distributions, and the gasfrom a large-scale numerical simulation. Special attention is paid to theradial profiles of the mass accretion rate and density. Both can be describedby a power-law function, $\dot{M}\propto r^s$ and $\rho\propto r^{-p}$. We findthat if the angular momentum is not very low, the value of $s$ is not sensitiveto the initial condition and lies within a narrow range, $0.47\la s \la 0.55$.However, the value of $p$ is more sensitive to the initial condition and liesin the range $0.48\la p \la 0.8$. The diversity of the density profile isbecause different initial conditions give different radial profiles of radialvelocity due to the different angular momentum of the initial conditions. Whenthe angular momentum of the accretion flow is very low, the inflow rate isconstant with radius. Taking the torus model as an example, we have alsoinvestigated the effects of inner and outer boundary conditions by consideringthe widely adopted "outflow" boundary condition and the "mass fluxconservation" condition. We find that the results are not sensitive to thesetwo boundary conditions.

On the role of initial and boundary conditions in numerical simulations of accretion flows