Diego Molteni

A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH

In literature, it is well know that the Smoothed Particle Hydrodynamics method can be affected by numerical noise on the pressure field when dealing with liquids. This can be highly dangerous when an SPH code is dynamically coupled with a structural solver. In this work a simple procedure is proposed to improve the computation of the pressure distribution in the dynamics of liquids. Such a procedure is based on the use of a density diffusion term in the equation for the mass conservation. This diffusion is a pure numerical effect, similar to the well known artificial viscosity originally proposed in SPH method to smooth out the shock discontinuities. As the artificial viscosity, the density diffusion used here goes to zero increasing the number of particles recovering consistency and convergence of the final numerical scheme adopted. Different artificial density diffusion formulas have been studied, paying attention to prevent unphysical changes of the flows. To show the improvements of the new scheme proposed here, a suitable set of examples, for which reference solutions or experimental data are available, has been tested.

Resonance oscillation of radiative shock waves in accretion disks around compact objects

We extend our previous numerical simulation of accretion disks with shock waves when cooling effects are also included. We consider bremsstrahlung and other power law processes:

Free-surface flows solved by means of SPH schemes with numerical diffusive terms

\Lambda \propto T^{\alpha} \rho^2

Three-dimensional numerical simulation of gaseous flow structure in semidetached binaries

to mimic cooling in our simulation. We employ {\it Smoothed Particle Hydrodynamics} technique as in the past. We observe that for a given angular momentum of the flow, the shock wave undergoes a steady, radial oscillation with the period is roughly equal to the cooling time. Oscillations seem to take place when the disk and cooling parameters (i.e., accretion rate, cooling process) are such that the infall time from shock is of the same order as the post-shock cooling time. The amplitude of oscillation could be up to ten percent of the distance of the shock wave from the black hole when the black hole is accreting. When the accretion is impossible due to the centrifugal barrier, the amplitude variation could be much larger. Due to the oscillation, the energy output from the disk is also seen to vary quasi-periodically. We believe that these oscillations might be responsible for the quasi periodic oscillation (QPO) behaviors seen in several black hole candidates, in neutron star systems as well as dwarf novae outbursts such as SS Cygni and VW Hyi.

SIMULATION OF THICK ACCRETION DISKS WITH STANDING SHOCKS BY SMOOTHED PARTICLE HYDRODYNAMICS

A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing the pressure field. Finally, an enhanced formulation for the second-order derivatives has been defined which is consistent and convergent all over the fluid domain and, therefore, permits to correctly model the diffusive terms up to the free surface. The model has been tested using different free surface flows clearly showing to be robust, efficient and accurate. An analysis of the CPU time cost and comparisons with the standard SPH scheme is provided.

Zero-Energy Rotating Accretion Flows near a Black Hole

The results of numerical simulation of mass transfer in semidetached non-magnetic binaries are presented. We investigate the morphology of gaseous flows on the basis of three-dimensional gas-dynamical calculations of interacting binaries of different types (cataclysmic variables and low-mass X-ray binaries). We find that taking into account a circumbinary envelope leads to significant changes in the stream–disc morphology. In particular, the obtained steady-state self-consistent solutions show an absence of impact between the gas stream from the inner Lagrangian point L1 and the forming accretion disc. The stream deviates under the action of the gas of the circumbinary envelope, and does not cause the shock perturbation of the disc boundary (traditional hotspot). At the same time, the gas of the circumbinary envelope interacts with the stream and causes the formation of an extended shock wave, located on the stream edge. We discuss the implication of this model without hotspot (but with a shock wave located outside the disc) for interpretation of the observations. The comparison of synthetic light curves with observations proves the validity of the discussed gas-dynamical model without hotspot. We have also considered the influence of the circumbinary envelope on the mass transfer rate in semidetached binaries. The obtained features of flow structure in the vicinity of L1 show that the gas of the circumbinary envelope plays an important role in the flow dynamics, and that it leads to significant (in order of magnitude) increase of the mass transfer rate. The most important contribution to this increase is from the stripping of the mass-losing star atmosphere by interstellar gas flows. The parameters of the formed accretion disc are also given in the paper. We discuss the details of the obtained gaseous flow structure for different boundary conditions on the surface of mass-losing star, and show that the main features of this structure in semidetached binaries are the same for different cases. The comparison of gaseous flow structure obtained in two- and three-dimensional approaches is presented. We discuss the common features of the flow structures and the possible reasons for revealed differences.

Smoothed particle hydrodynamics confronts theory : formation of standing shocks in accretion disks and winds around black holes

We present results of numerical simulation of inviscid thick accretion disks and wind flows around black holes. We use Smoothed Particle Hydrodynamics (SPH) technique for this purpose. Formation of thick disks are found to be preceded by shock waves travelling away from the centrifugal barrier. For a large range of the parameter space, the travelling shock settles at a distance close to the location obtained by a one-and-a-half dimensional model of inviscid accretion disks. Occasionally, it is observed that accretion processes are aided by the formation of oblique shock waves, particularly in the initial transient phase. The post-shock region (where infall velocity suddenly becomes very small) resembles that of the usual model of thick accretion disk discussed in the literature, though they have considerable turbulence. The flow subsequently becomes supersonic before falling into the black hole. In a large number of cases which we simulate, we find the formation of strong winds which are hot and subsonic when originated from the disk surface very close to the black hole but become supersonic within a few tens of the Schwarzschild radius of the blackhole. In the case of accretion of high angular momentum flow, very little amount of matter is accreted directly onto the black hole. Most of the matter is, however, first squeezed to a small volume close to the black hole, and subsequently expands and is expelled as a strong wind. It is quite possible that this expulsion of matter and the formation of cosmic radio jets is aided by the shock heating in the inner parts of the accretion disks.

Numerical simulations of standing shocks in accretion flows around black holes: a comparative study

We characterize the nature of thin, axisymmetric, inviscid accretion flows of cold adiabatic gas with zero specific energy in the vicinity of a black hole by the specific angular momentum. Using two-dimensional hydrodynamic simulations in cylindrical geometry, we present various regimes in which the accretion flows behave distinctly differently. When the flow has a small angular momentum (λ λb), most of the material is accreted into the black hole, forming a quasi-spherical flow or a simple disklike structure around it. When the flow has a large angular momentum (typically, larger than the marginally bound value, λ λmb), almost no accretion into the black hole occurs. Instead, the flow produces a stable standing shock with one or more vortices behind it and is deflected away at the shock as a conical, outgoing wind of higher entropy. If the flow has an angular momentum somewhat smaller than λmb (λu λ λmb), a fraction (typically 5%-10%) of the incoming material is accreted into the black hole, but the flow structure formed is similar to that for λ λmb. Some of the deflected material is accreted back into the black hole while the rest is blown away as an outgoing wind. These two cases with λ λu correspond those studied in the previous works by Molteni, Lanzafame, & Chakrabarti and Ryu et al. However, the flow with angular momentum close to the marginally stable value (λms) is found to be unstable. More specifically, if λb λ ~ λms λu, the flow displays a distinct periodicity in the sense that the inner part of the disk is built and destroyed regularly. The period is roughly equal to (4-6) × 103Rg/c, depending on the angular momentum of the flow. In this case, the internal energy of the flow around the black hole becomes maximum when the structure with the accretion shock and vortices is fully developed. But the mass accretion rate into the black hole reaches a maximum value when the structure collapses. Averaged over periods, more than half the incoming material is accreted into the black hole. We suggest the physical origin of these separate regimes from a global perspective. Then we discuss the possible relevance of the instability work to quasi-periodic oscillations.

The effect of cooling on time dependent behaviour of accretion flows around black holes

We present results of numerical simulation of thin accretion disks and winds. We use the smoothed particle hydrodynamics (SPH) technique for this purpose. We show that the simulation agrees very well with the recent theoretical work on the shock formation. The most significant conclusion is that shocks in an inviscid flow are extremely stable. For the first time, our work also removes the ambiguity in terms of the location and stability of shocks in adiabatic flows

On the Azimuthal Stability of Shock Waves around Black Holes

We compare the results of numerical simulations of thin and quasi-spherical (thick) accretion flows with existing analytical solutions. We use a Lagrangian code based on the Smooth Particle Hydrodynamics (SPH) scheme and an Eulerian finite difference code based on the Total Variation Diminishing (TVD) scheme. In one-dimensional thin flows, the results of the simulations, with or without shocks, agree very well with each other and with analytical solutions. In two-dimensional thick flows, the general features, namely the locations and strengths of centrifugal and turbulent pressure supported shocks, centrifugal barriers, and the funnel walls which are expected from analytical models, agree very well, though the details vary. Generally speaking, the locations of the shocks may be better obtained by SPH since the angular momentum is strictly preserved in SPH, but the shocks themselves are better resolved by TVD. The agreement of these code test results with analytical solutions provides us with confidence to apply these codes to more complex problems which we will discuss elsewhere.