An approach to the Riemann problem in the light of a reformulation of the state equation for SPH inviscid ideal flows: a highlight on spiral hydrodynamics in accretion discs

In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations if flow discontinuities (the Riemann problem) are to be solved. A necessary dissipation is normally used in such cases. An explicit artificial viscosity contribution is normally adopted to smooth out spurious heating and to treat transport phenomena. Such a treatment of inviscid flows is also widely adopted in the Smooth Particle Hydrodynamics (SPH) finite volume free Lagrangian scheme. In other cases, the intrinsic dissipation of Godunov-type methods is implicitly useful. Instead "shock tracking" methods normally use the Rankine-Hugoniot jump conditions to solve such problems. A simple, effective solution of the Riemann problem in inviscid ideal gases is here proposed, based on an empirical reformulation of the equation of state (EoS) in the Euler equations in fluid dynamics, whose limit for a motionless gas coincides with the classical EoS of ideal gases. The application of such an effective solution to the Riemann problem excludes any dependence, in the transport phenomena, on particle smoothing resolution length $h$ in non viscous SPH flows. Results on 1D shock tube tests, as well as examples of application for 2D turbulence and 2D shear flows are here shown. As an astrophysical application, a much better identification of spiral structures in accretion discs in a close binary (CB), as a result of this reformulation is also shown here.Comment: 19 pages, 17 figure

An approach for solving the boundary free edge difficulties in SPH modelling: application to a viscous accretion disc in close binaries

In this work, we propose a SPH interpolating Kernel reformulation suitable also to treat free edge boundaries in the computational domain. Application to both inviscid and viscous stationary low compressibility accretion disc models in Close Binaries (CB) are shown. The investigation carried out in this paper is a consequence of the fact that a low compressibility modelling is crucial to check numerical reliability. Results show that physical viscosity supports a well-bound accretion disc formation, despite the low gas compressibility, when a Gaussian-derived Kernel (from the Error Function) is assumed, in extended particle range - whose Half Width at Half Maximum (HWHM) is fixed to a constant $h$ value - without any spatial restrictions on its radial interaction (hereinafter GASPHER). At the same time, GASPHER ensures adequate particle interpolations at the boundary free edges. Both SPH and adaptive SPH (hereinafter ASPH) methods lack accuracy if there are not constraints on the boundary conditions, in particular at the edge of the particle envelope: Free Edge (FE) conditions. In SPH, an inefficient particle interpolation involves a few neighbour particles; instead, in the second case, non-physical effects involve both the boundary layer particles themselves and the radial transport. Either in a regime where FE conditions involve the computational domain, or in a viscous fluid dynamics, or both, a GASPHER scheme can be rightly adopted in such troublesome physical regimes. Despite the applied low compressibiity condition, viscous GASPHER model shows clear spiral pattern profiles demonstrating the better quality of results compared to SPH viscous ones. Moreover a successful comparison of results concerning GASPHER 1D inviscid shock tube with analytical solution is also reported.Comment: 18 pages, 12 figure

Simulation of Thick Accretion Disks with Standing Shocks by Smoothed Particle Hydrodynamics

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.Comment: LaTeX, 16 pages, Astrophysical Journal (in press

Spiral Patterns and Shocks in Low-compressibility Accretion Disks around Collapsed Objects: Two-dimensional SPH Modeling

In recent years contrasting results have been found regarding the onset of spiral structures and shock fronts in accretion disks around compact objects. Indeed, according to some authors, spiral structures and shock fronts do not develop if an adiabatic index γ > 1.16 is adopted. On the contrary, other authors obtain well-developed spiral patterns and shocks adopting γ = 1.2. In this paper, by using a smoothed particle hydrodynamics (SPH) code, we show that clear spiral patterns and strong radial shocks come out even in very low compressibility (γ = 1.3 > 1.16) accretion disk models in close binaries if the primary is a massive black hole (MBH) with a mass 30-60 times larger than the secondary, whatever the geometrical and dynamical conditions at the inner Lagrangian point, L1, may be, independent of sonic or subsonic injection flow boundary conditions. Indeed, the rationale of this work is that in close binary systems in which the primary is a MBH and the secondary is a low-mass star, we have enough initial energy and angular momentum at the inner Lagrangian point, L1, and a wide and deep enough primary potential well to favor the development of well-defined spiral structures, and eventually spiral shocks, independent of the gas compressibility. According to our results the presence of a MBH triggers the development of spiral structures and spiral shock fronts in the accretion disk both at its outer edge and in the disk bulk, because of the high particle concentration and the strong collisions induced by the strongly accelerated stream particles with the high initial angular momentum at L1

How initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non viscous SPH simulations

Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, inviscid 2D simulations are performed, using the SPH method, to study the migration of one protoplanet, to evaluate the effectiveness of the accretion disc in the protoplanet dragging towards the central star, as a function of the mass of the planet itself, of disc tangential kinematics. To this purpose, the SPH scheme is considered suitable to study the roles of turbulence, kinematic and boundary conditions, due to its intrinsic advective turbulence, especially in 2D and in 3D codes. Simulations are performed both in disc sub-Keplerian and in Keplerian kinematic conditions as a parameter study of protoplanetary migration if moderate and consistent deviations from Keplerian Kinematics occur. Our results show migration times of a few orbital periods for Earth-like planets in sub-Keplerian conditions, while for Jupiter-like planets estimates give that about $10^4$ orbital periods are needed to half the orbital size. Timescales of planet migration are strongly dependent on the relative position of the planet with respect to the shock region near the centrifugal barrier of the disc flow.Comment: 12 pages, 18 figures, under review by MNRA

Dyke Emplacement and Hazard at Stromboli

In February 2007, two effusive vents opened along the flank of Sciara del Fuoco (SdF) depression at Stromboli. The summit craters collapsed, obstructing the central conduit, choking the vents and increasing the deformation within SdF. Here a new vent opened, releasing the excess magmatic pressure. The eruption continued, after a summit explosion, until April. The vents were fed by laterally propagating dykes. Vent location is similar to that of the 2002-2003 eruption, fed by dykes triggering landslides, which in turn produced a tsunami. However, the 2007 eruption did not develop landslides, suggesting that their triggering also depends on other factors, (i.e. magmatic pressure)

Trend Analysis of Air Quality Index in Catania from 2010 to 2014

Abstract Information on air quality in urban areas represents an important objective to raise awareness and participation of citizens towards those measures aimed at containing and reducing vehicular traffic. For several years at the international level, evaluation procedures have been adopted by indices. One of the first synthetic indices, adopted by the United States Environmental Protection Agency (US-EPA), was the Pollution Standard Index (PSI). In 1999, the EPA replaced the PSI index with Air Quality Index (AQI), which includes two new sub-indices, the ozone at ground level and fine particulate. Despite the European Decisions 97/101/EC and 2001/752/EC, have established an exchange of information from networks and individual stations measuring ambient air pollution in Member States, the use of a single index has not yet been defined that allows you to compare different realities. This heterogeneity emerges in Italy as well, where only a few Environmental Protection Agencies disclose indexes to inform citizens. In this article, the Air Quality Index (AQI) currently used by the United States Environmental Protection Agency has been applied to the metropolitan city of Catania, in order to analyze the level of pollution daily from 2010 to 2014. Through the use of the AQI it was possible to synthesize in a single daily value, concentrations of major pollutants in urban areas (NO2, O3, CO, SO2, PM10) for the entire period. For the calculation procedure of the AQI, the data concentrations were provided by Municipal Ecology and Environment Office. The data relates to three monitoring stations, whose locations have not changed over the years. This also made it possible to evaluate the change in frequency of AQI agglomerations where the monitoring units have been positioned. The value obtained by the AQI for each station has been ranked in six levels of pollution; each level has been associated with a particular coloring allowing this information to be more intuitive. Lastly, it was possible to reach the air quality assessment in urban environment from the frequency variations of each level derived from the year 2010 until 2014