Smoothed Particle Hydrodynamics with Smoothed Pseudo-Density

In this paper, we present a new formulation of smoothed particle hydrodynamics (SPH), which, unlike the standard SPH (SSPH), is well-behaved at the contact discontinuity. The SSPH scheme cannot handle discontinuities in density (e.g. the contact discontinuity and the free surface), because it requires that the density of fluid is positive and continuous everywhere. Thus there is inconsistency in the formulation of the SSPH scheme at discontinuities of the fluid density. To solve this problem, we introduce a new quantity associated with particles and density of that quantity. This density evolves through the usual continuity equation with an additional artificial diffusion term, in order to guarantee the continuity of density. We use this density or pseudo density, instead of the mass density, to formulate our SPH scheme. We call our new method as SPH with smoothed pseudo-density (SPSPH). We show that our new scheme is physically consistent and can handle discontinuities quite well.

Density Independent Smoothed Particle Hydrodynamics for Non-Ideal Equation of State

The smoothed particle hydrodynamics (SPH) method is a useful numerical tool for the study of a variety of astrophysical and planetlogical problems. However, it turned out that the standard SPH algorithm has problems in dealing with hydrodynamical instabilities. This problem is due to the assumption that the local density distribution is differentiable. In order to solve this problem, a new SPH formulation, which does not require the differentiability of the density, have been proposed. This new SPH method improved the treatment of hydrodynamical instabilities. This method, however, is applicable only to the equation of state (EOS) of the ideal gas. In this paper, we describe how to extend the new SPH method to non-ideal EOS. We present the results of various standard numerical tests for non-ideal EOS. Our new method works well for non-ideal EOS. We conclude that our new SPH can handle hydrodynamical instabilities for an arbitrary EOS and that it is an attractive alternative to the standard SPH.

Flaring up of the Compact Cloud G2 during the Close Encounter with Sgr A*

A compact gas cloud G2 is predicted to reach the pericenter of its orbit around the super massive black hole (SMBH) of our galaxy, Sagittarius A* (Sgr A*). This event will give us a rare opportunity to observe the interaction between SMBH and gas around it. We report the result of the fully three-dimensional simulation of the evolution of G2 during the first pericenter passage. The strong tidal force by the SMBH stretches the cloud along its orbit, and compresses it strongly in the vertical direction, resulting in the heating up and flaring up of the cloud. The bolometric luminosity will reach the maximum of $sim100 L_{odot}$. This flare should be easily observed in the near infrared.