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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.
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 ins
We present Phantom, a fast, parallel, modular and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on
We present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method (SPMHD) with the geometric density average force expression (GDSPH). We perform shearing box simulations with different initial setups and a wide
The standard formulation of the smoothed particle hydrodynamics (SPH) assumes that the local density distribution is differentiable. This assumption is used to derive the spatial derivatives of other quantities. However, this assumption breaks down a
At present, the giant impact (GI) is the most widely accepted model for the origin of the Moon. Most of the numerical simulations of GI have been carried out with the smoothed particle hydrodynamics (SPH) method. Recently, however, it has been pointe