SPH compressible turbulence

By Joseph J Monaghan. 2002

205 citations recorded by the source corpus.

In this paper a smoothed particle hydrodynamics (SPH) version of the alpha turbulence model devised by Holm and his colleagues is formulated for compressible flow with a resolution that varies in space and time. The alpha model involves two velocity fields. One velocity field is obtained from the momentum equation, the other by averaging this velocity field as in the version of SPH called XSPH. The particles (fluid elements) are moved with the averaged velocity. In analogy to the continuum alpha model we obtain a particle Lagrangian from which the SPH alpha equations can be derived. The system satisfies a discrete Kelvin circulation theorem identical to that obtained with no velocity averaging. In addition, the energy, linear and angular momentum are conserved. We show that the continuum equivalent of the SPH equations are identical to the continuum alpha model, and we conjecture that they will have the same desirable features of the continuum model including the reduction of energy in the high-wavenumber modes even when the dissipation is zero. Regardless of issues concerning turbulence modelling, the SPH alpha model is a powerful extension of the XSPH algorithm, which reduces disorder at short length-scales and retains the constants of the motion. The SPH alpha model is simple to implement.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/ae9365179f147b0095b55d07f3bc4c4eab3a262e

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In Computational Mechanics

Citations in the corpus

Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics (2017, unknown): “Several spheroidal components are available, including the potentials of Plummer (1911), Hernquist (1990) and Hubble (1930).”
Smoothed particle hydrodynamics with radiative transfer in the flux-limited diffusion approximation (2004, background): “Recently, a reformulation of the SPH equations has allowed both energy and entropy to be conserved simultaneously (Inutsuka & Imaeda 2001; Springel & Hernquist 2002; Monaghan 2002).”
Remnant evolution after a carbon–oxygen white dwarf merger (2007, methodology): “Note that this could, in principle, be improved even further by taking into accoun t the so-called “grad-h”-terms (Springel & Hernquist 2002; Mona gh n 2002; Price 2004) and extra-terms arising from adapting gra vitational smoothing terms (Price & Monaghan 2006). To avoid numerical artifacts, we onl”
On the treatment of entropy mixing in numerical cosmology (2008, methodology): “It is the expectation of the authors that more rigorously derived models, such as an SPH implementation of the alpha turbulence model (Monaghan 2002), will ultimately provide a robust turbulent modelling capability for SPH. AC K N OW L E D G M E N T S The authors would like to acknowledge the…”
TIDAL DISRUPTION AND IGNITION OF WHITE DWARFS BY MODERATELY MASSIVE BLACK HOLES (2008, background): “Note that this could, in principle, be improved even further by taking into account the so-called “grad-h”-terms (Springel & Hernquist 2002; Monaghan 2002) and extra-terms arising from adapting gravitational smoothing terms (Price & Monaghan 2007).”
Smoothed Particle Hydrodynamics in Astrophysics (2010, methodology): “We start by discretizing the Lagrangian in terms of fluid particles of massmi, yielding LSPH= ∑ i ( 1 2 miv2i −miui ) , (12) where it has been assumed that the thermal energy per unit mass of particle can be expressed through an entropic functionAi of the particle, which simply labels its specific t”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, background): “We thank Volker Springel, Romain Teyssier, Lars Hernquist, Jim Stone, Dusan Keres, Paul Duffell, James Wadsley, Oscar Agertz, Thorsten Naab, Richard Bower, Matthieu Schaller, Nick Gnedin, Andrey Kravtsov, Desika Narayanan, Ji-Hoon Kim, Andrew Wetzel, Eliot Quataert, Paul Torrey, Norm Murray, Claude-”
NEUTRINO SIGNATURES AND THE NEUTRINO-DRIVEN WIND IN BINARY NEUTRON STAR MERGERS (2008, background): “• A self-consistent treatment of extra terms in the hydrodynamics equations that arise from varying smoothing lengths (so-called “grad-h”-terms; Springel & Hernquist 2002; Monaghan 2002; Price 2004; Rosswog & Price 2007).”
An MHD gadget for cosmological simulations (2008, background): “Examples include are more modern formulations of the artificial viscosity (Monaghan 1997), the introduction of self-consistent correction terms from varying smoothing length (Springel & Hernquist 200 ; Monaghan 2002) or the continuous definition of the smoothing length (Springel & Hernquist 2002).”
The impact of magnetic fields on single and binary star formation (2007, unknown): “…+ Pj + 1 2µ0 B2j Ωjρ2j ∇µWij(hj) # + X j mj (BµBν)i − (B µBν)j µ0ρiρj ∇νWij , (12) wherevi, ρi, Pi and Bi refer to the density, pressure and magnetic field of particlei andΩ is a normalisation term related to the gradient of the smoothing length (as in, e.g. Monaghan 2002; Price & Monaghan 2006).”
The effect of magnetic fields on star cluster formation (2008, methodology): “…algorithms, most notably by adopting the energy and entropy-conserving variable smoothing length algorithmsdeveloped by Springel & Hernquist (2002), Monaghan (2002) and Price & Monaghan (2004b) and by the introduction of additional physics in the form of magnetic fields (Price & Bate 2007) and…”
Improving convergence in smoothed particle hydrodynamics simulations without pairing instability (2012, unknown): “…∑ j mj [ P̂i i ρ̂ 2 i ∇iW (xij , hi)+ P̂j j ρ̂ 2 j ∇iW (xij , hj ) ] , (3) where xij = xi − xj and P̂i = ρ̂2i ∂u/∂ρ̂i , while the factors i = 1 νhνi ρ̂i ∂(hνi ρ̂i) ∂ ln hi 1 (4) (Monaghan 2002; Springel & Hernquist 2002) arise from the adaption of hi (Nelson & Papaloizou) such that hνi ρ̂i =…”
SPLASH: An Interactive Visualisation Tool for Smoothed Particle Hydrodynamics Simulations (2007, background): “…is a spatially variable quantity set in such a way as either to fix (either exactly or approximately) the number of nearest neighbours (Hernquist & Katz 1989; Benz et al. 1990), or via an analytic relation to the (number) density (Springel & Hernquist 2002; Monaghan 2002; Price & Monaghan 2007).”
Science with ASKAP (2008, background): “Many numerical simulations have been done or are ungoing to alleviate this situation but they neglect many constraints relevant to the ISM that would make them realistic [8, 9, 198].”
Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH (2007, methodology): “…standard derivation of the SPH equations from a Lagrangian variational principle has been presented by many authors (e.g. Nelson and Papaloizou, 1994; Monaghan and Price, 2001; Springel and Hernquist, 2002; Monaghan, 2002; Price and Monaghan, 2004b), it is instructive to repeat the derivation here.”
Improved SPH methods for simulating free surface flows of viscous fluids (2009, background): “geophysical flows [1,8,38], turbulence modeling [33], viscoelastic flows [13,14], and free surface viscoelastic flows [16].”
Smoothed Particle Magnetohydrodynamics – II. Variational principles and variable smoothing-length terms (2003, methodology): “…multipliers; however, in the context of the discussion given in Section 3 we note that by expressing the smoothing length as a function of ρ we can therefore specify h as a function of the particle coordinates (Monaghan 2002); that is, we have h = h(ρ) where ρ is given by ρa = ∑ b mbW (rab, ha).”
Smoothed particle hydrodynamics and magnetohydrodynamics (2010, background): “Since in turn density is itself a function of smoothing length, this leads to the idea of an iterative summation to simultaneously obtain the (mutually dependent) q(r) and h(r) [62,89,99].”