Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH

By Daniel J. Price. Journal of Computational Physics, 2007

340 citations recorded by the source corpus.

In this paper we discuss the treatment of discontinuities in smoothed particle hydrodynamics (SPH) simulations. In particular we discuss the difference between integral and differential representations of the fluid equations in an SPH context and how this relates to the formulation of dissipative terms for the capture of shocks and other discontinuities. This has important implications for many problems, in particular related to recently highlighted problems in treating Kelvin-Helmholtz instabilities across entropy gradients in SPH. The specific problems pointed out by Agertz et al. [O. Agertz, B. Moore, J. Stadel, D. Potter, F. Miniati, J. Read, L. Mayer, A. Gawryszczak, A. Kravtsov, A. Nordlund, F. Pearce, V. Quilis, D. Rudd, V. Springel, J. Stone, E. Tasker, R. Teyssier, J. Wadsley, R. Walder, Fundamental differences between SPH and grid methods, MNRAS 380 (2007) 963-978] are shown to be related in particular to the (lack of) treatment of contact discontinuities in standard SPH formulations which can be cured by the simple application of an artificial thermal conductivity term. We propose a new formulation of artificial thermal conductivity in SPH which minimises dissipation away from discontinuities and can therefore be applied quite generally in SPH calculations.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/a0a7744641a1940ddb1b46b5a8f747af77a753cc

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Citations in the corpus

Inviscid smoothed particle hydrodynamics (2010, background): “…contact discontinuity at x = 0.138 common to all schemes tested are not related to artificial viscosity (the irregularities in α at that point could be removed by choosing non-zero initial α at the initial discontinuity); they can be alleviated by artificial conductivity (Price 2004; Price 2008).”
Molecular hydrogen abundances of galaxies in the EAGLE simulations (2015, positive): “…SPH described in Hopkins (2013), (ii) the artificial viscosity switch of Cullen & Dehnen (2010), (iii) an artificial conduction switch described in Price (2008), (iv) a C2 Wendland (1995) kernel with 58 neighbours to interpolate SPH properties across neighbouring particles, and (v) the timestep…”
E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh (2009, background): “While it is possible to alleviate these effects by introducing artificial heat conduction or mixing terms (Price, 2008; Wadsley et al., 2008), or a modified treatment of the artificial viscosity (Dolag et al., 2005), it is still unclear whether any of these suggestions provides a universal solution…”
Smoothed Particle Hydrodynamics in Astrophysics (2010, background): “…entropy, but for this no source is foreseen in the entropy-conserving formulation of standard SPH. Including artificial thermal conduction (as in Price, 2008) is one interesting approach to address this problem, as this process equilibrates the temperatures while conserving energy and…”
An Hamiltonian interface SPH formulation for multi-fluid and free surface flows (2009, methodology): “[9,12]), or equivalently following the variational principle used by Bonet and Lok [5].”
Stellar and Quasar Feedback in Concert: Effects on AGN Accretion, Obscuration, and Outflows (2015, methodology): “We note that all simulations employ the more sophisticated formulation of artificial viscosity described in Morris & Monaghan (1997), which greatly reduces numerical dissipation away from shocks relative to earlier implementations (see e.g. Rosswog et al. 2000; Price 2008).”
RADIATION-HYDRODYNAMIC SIMULATIONS OF THE FORMATION OF ORION-LIKE STAR CLUSTERS. II. THE INITIAL MASS FUNCTION FROM WINDS, TURBULENCE, AND RADIATION (2012, background): “…an overestimate of the difference between the two simulation methods, because, while formally the SPH simulations have vacuum outside their clouds, SPH creates an artificial surface tension at density discontinuities (Price 2008), and this will act very much like a confining external pressure.”
Astrophysical smooth particle hydrodynamics (2009, methodology): “A modification of artificial dissipation terms (Price, 2008) or, alternatively, a more general formulation of the SPH equations (Read et al.”
Moving mesh cosmology: numerical techniques and global statistics (2011, background): “For example, changes to the computation of smoothed pressure gradients (Abel 2011) or the addition of an artificial thermal conductivity to the equations of motion (e.g. Price 2008) enable SPH to better handle shearing interfaces and the onset of Kelvin– Helmholtz instabilities.”
The EAGLE project: Simulating the evolution and assembly of galaxies and their environments (2014, methodology): “We use the artificial viscosity switch from Cullen & Dehnen (2010) and a switch for artificial conduction similar to that of Price (2008).”
The eagle simulations of galaxy formation: Public release of halo and galaxy catalogues (2015, background): “that vary: n H,0, nn, C visc and T AGN (see section 4 of Schaye et al. (2015) for an explanation of their meaning). Cullen and Dehnen (2010) and a weak thermal conduction term of the form proposed by Price (2008). The eects of this state-of-the-art formulation of SPH on the galaxy properties is expl”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, methodology): “We note that all SPH variants shown include the “artificial conductivity” (entropy diffusion term) above, which has been argued to eliminate such spurious structures (see Price 2008; Wadsley et al. 2008; Read & Hayfield 2012); we will discuss this further below.”
NIHAO project – I. Reproducing the inefficiency of galaxy formation across cosmic time with a large sample of cosmological hydrodynamical simulations (2015, methodology): “The treatment of artificial viscosity has been modified to use the signal velocity as described in Price (2008).”
Colours and luminosities of z = 0.1 galaxies in the eagle simulation (2015, methodology): “…to use the conservative pressure-entropy SPH formulation of Hopkins (2013), the artificial viscosity switch introduced by Cullen & Dehnen (2010), an artificial conduction switch inspired by Price (2008), the C2 kernel from Wendland (1995) and the timestep limiter of Durier & Dalla Vecchia (2012).”
An improved SPH scheme for cosmological simulations (2015, background): “…energy for each particle and its neighbours is then given by dui dt ∣∣∣∣ cond = ∑ j mj ρij (uj − ui)αcij vsig,cij F ij , (26) where we employ the choice of Price (2008) for signal velocity depending on the pressure gradient of the form v sig,c ij = √ |Pi − Pj | ρij (27) and αcij = (αci + αcj…”
Gasoline2: a modern smoothed particle hydrodynamics code (2017, methodology): “We note that alternate, stronger forms of diffusion such as the artificial conduction of Price (2008) also improve results on this test even with more traditional pressure gradients.”
Bimodality of low-redshift circumgalactic O VI in non-equilibrium EAGLE zoom simulations (2016, background): “…SPH formulation described by Hopkins (2013), ii) the artificial viscosity switch of Cullen & Dehnen (2010), iii) the artificial conduction switch of Price (2008), iv) the timestep limiter from Durier & Dalla Vecchia (2012) to improve energy conservation during sudden changes of internal energy,…”
Moving mesh cosmology: the hydrodynamics of galaxy formation (2011, methodology): “There have been a number of attempts to improve the description of mixing in SPH by modifying the standard set of discretized equations (see e.g. Price 2008; Wadsley, Veeravalli & Couchman 2008; Heß & Springel 2010) or by incorporating a Riemann solver in place of the artificial viscosity (e.g.…”
Shocking results without shocks: Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations (2011, methodology): “Some extensions and improvements of the standard SPH formulation that go into this direction have already been proposed (e.g. Price 2008; Heß & Springel 2010; Cullen & Dehnen 2010; Read et al. 2010; Read & Hayfield 2011; Abel 2011).”
Smoothed particle hydrodynamics and magnetohydrodynamics (2010, methodology): “…variables are the density, specific momentum and energy (ρ, v and e = 12v 2 + u respectively), and the terms take the form9 (Monaghan, 1997; Price, 2008)( dva dt ) diss = ∑ b mb αvsig(va − vb) · r̂ab ρ̄ab r̂abFab, (101)( dea dt ) diss = ∑ b mb (e∗a − e∗b) ρ̄ab Fab, (102) 9Note that in SPH…”