A new prescription for viscosity in Smoothed Particle Hydrodynamics

Watkins, S. J.; Bhattal, A. S.; Francis, N.; Turner, J. A.; Whitworth, Anthony Peter

doi:10.1051/aas:1996104

Cited by 72 publications

(69 citation statements)

References 19 publications

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“…Therefore we have repeated the shocktube simulation including the du dt term. The initial conditions and method used are described in Watkins et al (1996). When using the artificial viscosity, the rate of change of internal energy, due to pressure and viscous forces, is given by (Monaghan 1992) …”

Section: Discussionmentioning

confidence: 99%

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Numerical simulations of protostellar encounters - I. Star-disc encounters

Boffin¹,

Watkins²,

Bhattal³

et al. 1998

Monthly Notices RAS

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101

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It appears that most stars are born in clusters, and that at birth most stars have circumstellar discs which are comparable in size to the separations between the stars. Interactions between neighbouring stars and discs are therefore likely to play a key rôle in determining disc lifetimes, stellar masses, and the separations and eccentricities of binary orbits. Such interactions may also cause fragmentation of the discs, thereby triggering the formation of additional stars.We have carried out a series of simulations of disc-star interactions using an SPH code which treats self-gravity, hydrodynamic and viscous forces. We find that interactions between discs and stars provide a mechanism for removing energy from, or adding energy to, the orbits of the stars, and for truncating the discs. However, capture during such encounters is unlikely to be an important binary formation mechanism.A more significant consequence of such encounters is that they can trigger fragmentation of the disc, via tidally and compressionally induced gravitational instabilities, leading to the formation of additional stars. When the disc-spins and stellar orbits are randomly oriented, encounters lead to the formation of new companions to the original star in 20% of encounters. If most encounters are prograde and coplanar, as suggested by simulations of dynamically-triggered star formation, then new companions are formed in approximately 50% of encounters.

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Section: Discussionmentioning

confidence: 99%

“…We also include the β-term from the artificial viscosity with β = 1 (seeMonaghan (1989)). We have performed a variety of tests on this viscosity prescription, and they are reported in Watkins et al (1996). Initially the numerical Reynolds number in the discs is ∼ 3000(r/1000AU) −1/2 .…”

Section: Methodsmentioning

confidence: 99%

Numerical simulations of protostellar encounters - I. Star-disc encounters

Boffin¹,

Watkins²,

Bhattal³

et al. 1998

Monthly Notices RAS

Self Cite

101

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“…Since its invention, it has been extensively studied, extended and applied in many areas such as the dynamic response of elasto-plastic materials [18][19][20], free surface flows [21], low-Reynolds number viscous flows [22][23][24], solid friction [25], incompressible fluids [26,27], heat transfer [28], multi-phase flows [29,30], geophysical flows [31][32][33] and turbulence modeling [34]. Solid friction has often been studied using embedded atom methods, a method very similar in spirit to SPH [35].…”

Section: Introductionmentioning

confidence: 99%

A numerical study of the SPH method for simulating transient viscoelastic free surface flows

Fang

Owens

Tacher

et al. 2006

Journal of Non-Newtonian Fluid Mechanics

142

121

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The smoothed particle hydrodynamics (SPH) method is extended and tested for the numerical simulation of transient viscoelastic free surface flows. The basic equations governing the free surface flow of an Oldroyd-B fluid are considered and approximated by SPH. In particular, a drop of an Oldroyd-B fluid impacting a rigid plate is simulated. Results for a Newtonian fluid are also presented for comparison. It is found that the original SPH method, which has been successfully applied to the simulation of transient viscoelastic flows in bounded domains (such as the start-up flow between parallel plates), is unable to simulate the viscoelastic free surface flow considered here because of the so-called tensile instability. This instability leads to unrealistic fracture and particle clustering in fluid stretching and may eventually result in complete blowup of the simulation. Recent works have shown that in simulations of elastic solids the tensile instability can be removed by an artificial stress. Here we show that the same idea also works for viscoelastic fluids provided that the constant parameter entering in the definition of the artificial stress is properly chosen. Numerical results obtained are in good agreement with those simulated by a finite difference technique.

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“…α and β are two free parameters, of the order of unity, which account respectively for the shear and bulk viscosity in the Navier-Stokes equation (Watkins et al 1996), and for the von Neuman-Richtmyer viscosity, which works in high Mach number flows. A more recent formulation is the so-called "signal velocity" viscosity (Monaghan 1997), which works better for small pair separations between particles, being a first-order expression of h/r; it reads…”

Section: Discontinuities 331 Artificial Viscositymentioning

confidence: 99%

EvoL: the new Padova Tree-SPH parallel code for cosmological simulations

Merlin¹,

Buonomo

Piovan

et al. 2010

A&A

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Context. We present the new release of the Padova N-body code for cosmological simulations of galaxy formation and evolution, EvoL. The basic Tree + SPH code is presented and analysed, together with an overview of the software architectures. Aims. EvoL is a flexible parallel Fortran95 code, specifically designed for simulations of cosmological structure formations on cluster, galactic and sub-galactic scales. Methods. EvoL is a fully Lagrangian self-adaptive code, based on the classical oct-tree by Barnes & Hut (1986, Nature, 324, 446) and on the smoothed particle hydrodynamics algorithm (SPH, Lucy 1977, AJ, 82, 1013. It includes special features like adaptive softening lengths with correcting extra-terms, and modern formulations of SPH and artificial viscosity. It is designed to be run in parallel on multiple CPUs to optimise the performance and save computational time. Results. We describe the code in detail, and present the results of a number of standard hydrodynamical tests.

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A new prescription for viscosity in Smoothed Particle Hydrodynamics

Cited by 72 publications

References 19 publications

Numerical simulations of protostellar encounters - I. Star-disc encounters

Numerical simulations of protostellar encounters - I. Star-disc encounters

A numerical study of the SPH method for simulating transient viscoelastic free surface flows

EvoL: the new Padova Tree-SPH parallel code for cosmological simulations

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