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Register a new userA Formulation of Consistent Particle Hydrodynamics in Strong Form
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In fluid dynamical simulations in astrophysics, large deformations are common and surface tracking is sometimes necessary. Smoothed Particle Hydrodynamics (SPH) method has been used in many of such simulations. Recently, however, it has been shown that SPH cannot handle contact discontinuities or free surfaces accurately. There are several reasons for this problem. The first one is that SPH requires that the density is continuous and differentiable. The second one is that SPH does not have the consistency, and thus the accuracy is zeroth order in space. In addition, we cannot express accurate boundary conditions with SPH. In this paper, we propose a novel, high-order scheme for particle-based hydrodynamics of compress- ible fluid. Our method is based on kernel-weighted high-order fitting polynomial for intensive variables. With this approach, we can construct a scheme which solves all of the three prob- lems described above. For shock capturing, we use a tensor form of von-Neumann-Richtmyer artificial viscosity. We have applied our method to many test problems and obtained excel- lent result. Our method is not conservative, since particles do not have mass or energy, but only their densities. However, because of the Lagrangian nature of our scheme, the violation of the conservation laws turned out to be small. We name this method Consistent Particle Hydrodynamics in Strong Form (CPHSF).
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We present a fix to the overdamping problem found by Laibe & Price (2012) when simulating strongly coupled dust-gas mixtures using two different sets of particles using smoothed particle hydrodynamics. Our solution is to compute the drag at the barycentre between gas and dust particle pairs when computing the drag force by reconstructing the velocity field, similar to the procedure in Godunov-type solvers. This fixes the overdamping problem at negligible computational cost, but with additional memory required to store velocity derivatives. We employ slope limiters to avoid spurious oscillations at shocks, finding the van Leer Monotonized Central limiter most effective.
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 at the contact discontinuity. At the contact discontinuity, the density of the low-density side is overestimated while that of the high-density side is underestimated. As a result, the pressure of the low (high) density side is over (under) estimated. Thus, unphysical repulsive force appears at the contact discontinuity, resulting in the effective surface tension. This tension suppresses fluid instabilities. In this paper, we present a new formulation of SPH, which does not require the differentiability of density. Instead of the mass density, we adopt the internal energy density (pressure), and its arbitrary function, which are smoothed quantities at the contact discontinuity, as the volume element used for the kernel integration. We call this new formulation density independent SPH (DISPH). It handles the contact discontinuity without numerical problems. The results of standard tests such as the shock tube, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, point like explosion, and blob tests are all very favorable to DISPH. We conclude that DISPH solved most of known difficulties of the standard SPH, without introducing additional numerical diffusion or breaking the exact force symmetry or energy conservation. Our new SPH includes the formulation proposed by Ritchie & Thomas (2001) as a special case. Our formulation can be extended to handle a non-ideal gas easily.
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 stellar, galactic, planetary and high energy astrophysics and has already been used widely for studies of accretion discs and turbulence, from the birth of planets to how black holes accrete. Here we describe and test the core algorithms as well as modules for magnetohydrodynamics, self-gravity, sink particles, H_2 chemistry, dust-gas mixtures, physical viscosity, external forces including numerous galactic potentials as well as implementations of Lense-Thirring precession, Poynting-Robertson drag and stochastic turbulent driving. Phantom is hereby made publicly available.
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 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.
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