Improving convergence in smoothed particle hydrodynamics simulations without pairing instability

By W. Dehnen, H. Aly. 2012

628 citations recorded by the source corpus.

The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number NH of neighbours when switching to more extended smoothing kernels at fixed resolution (using an appropriate definition for the SPH resolution scale) is insufficient to combat these errors. Consequently, trading resolution for better convergence is necessary, but for traditional smoothing kernels this option is limited by the pairing (or clumping) instability. Therefore, we investigate the suitability of the Wendland functions as smoothing kernels and compare them with the traditional B-splines. Linear stability analysis in three dimensions and test simulations demonstrate that the Wendland kernels avoid the pairing instability for all NH, despite having vanishing derivative at the origin (disproving traditional ideas about the origin of this instability/ instead, we uncover a relation with the kernel Fourier transform and give an explanation in terms of the SPH density estimator). The Wendland kernels are computationally more convenient than the higher-order B-splines, allowing large NH and hence better numerical convergence (note that computational costs rise sub-linear with NH). Our analysis also shows that at low NH the quartic spline kernel with NH ~= 60 obtains much better convergence then the standard cubic spline.

Subfields: Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/1133b9e644d85c2534b915606b1dc447b76c5845

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Citations in the corpus

Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future (2016, background): “Recently, Dehnen and Aly (2012) studied the so-called pairing instability process in 3-”
A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems (2012, methodology): “Our favored kernel is taken from more detailed kernel comparison studies in Hongbin & Xin (2005); Dehnen & Aly (2012); however, unlike some other SPH formulations, we find that even the “simplest” kernel possible (NNGB = 32 cubic spline) reproduces good results in several tests, except in the…”
Baryon impact on the halo mass function: Fitting formulae and implications for cluster cosmology (2015, background): “…entropy-conserving formulation of SPH (Springel & Hernquist 2002) and a higher order kernel based on the biascorrected, sixth-order Wendland kernel (Dehnen & Aly 2012) with 295 neighbours, which together with a low-viscosity SPH scheme allows us to properly track turbulence within galaxy clusters…”
Size evolution of normal and compact galaxies in the EAGLE simulation (2015, background): “…includes the Hopkins (2013) pressureentropy formulation, a time-step limiter (Durier & Dalla Vecchia 2012), artificial viscosity and conduction (Dehnen & Aly 2012), and the Wendland (1995) C2 kernel; this set of changes to the SPH is collectively referred to as ANARCHY (see appendix A of…”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “8, but much slower, as ∼ N−0.6; again a similar scaling is seen in the Gresho problem (Dehnen & Aly 2012, Fig.”
Galaxies on FIRE (Feedback In Realistic Environments): stellar feedback explains cosmologically inefficient star formation (2013, methodology): “However we have also experimented with the Wendland kernels in Dehnen & Aly (2012) and triangular kernels in Read et al. (2010) and see no significant improvements up to neighbor numbers∼ 500.”
Bimodality of low-redshift circumgalactic O VI in non-equilibrium EAGLE zoom simulations (2016, background): “…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, and v) a C2 Wendland (1995) 58-neighbour kernel to suppress particle-pairing instabilities (Dehnen & Aly 2012).”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, methodology): “’s method, by incorporating the ECS and DS schemes for the fluid phase as well as applying a Wendland kernel (Wendland 1995; Dehnen and Aly 2012) for calculation of fluid forces on structure.”
Numerical simulation of Laser Fusion Additive Manufacturing processes using the SPH method (2018, methodology): “It has been demonstrated to be the optimal kernel choice for numerical stability of the SPH method [38].”
MUFASA: Galaxy Formation Simulations With Meshless Hydrodynamics (2016, methodology): “Metal-line cooling is computed using Cloudy (Ferland 2004) tables self-consistently includ- 2 Dehnen & Aly (2012) found that SPH similar to T-SPH using a cubic spline kernel with 64 neighbors may, in strong shearing flows, be subject to particle pairing instabilities that result in lowering the…”
A Superbubble Feedback Model for Galaxy Simulations (2014, methodology): “For the tests shown here we used the Wendland C2 kernel detailed in Dehnen & Aly (2012) with 64 neigbours where the SPH smoothing distance is defined so that the kernel weight drops to zero at 2h. Sharp density contrasts, as seen in highly resolved superbubbles, can require additional checks on the…”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, methodology): “Following Dehnen & Aly (2012), the acceleration from each particle is constructed assuming its mass distribution follows the kernel function; if we assume the correct background is a uniform density field, then discretize this into particles, it is straightforward to compute the fractional…”
NIHAO project – I. Reproducing the inefficiency of galaxy formation across cosmic time with a large sample of cosmological hydrodynamical simulations (2015, methodology): “To avoid pair instabilities, ESF-gasoline2 uses the Wendland C2 function for its smoothing kernel (Dehnen & Aly 2012).”
The EAGLE simulations of galaxy formation: the importance of the hydrodynamics scheme (2015, methodology): “More accurate estimators for both the field quantities and their derivatives can be obtained by using Wendland (1995) kernels (Dehnen & Aly 2012).”
Neutral hydrogen in galaxy haloes at the peak of the cosmic star formation history (2014, methodology): “Our simulations employ an adaptive fifth-order spline kernel 5 http://www.tapir.caltech.edu/∼phopkins/Site/GIZMO.html with a neighbor number Nngb ≈ 60 designed to optimally resolve sound waves down to a wavelength of order the gas smoothing length (Dehnen & Aly 2012).”
Gasoline2: a modern smoothed particle hydrodynamics code (2017, background): “This issue was fully resolved by Dehnen & Aly (2012), who showed the origin of the pairing and that Wendland (1995) smoothing kernels do not suffer from it.”
An improved SPH scheme for cosmological simulations (2015, methodology): “As vertical lines, we show the Nyqvist frequency kNyq = Nkmin, the WC4 smoothing scale kσ and the WC4 kernel compact support khsml = π/hsml (Dehnen & Aly 2012).”
Stellar and Quasar Feedback in Concert: Effects on AGN Accretion, Obscuration, and Outflows (2015, background): “…appear robust to these variations. improvements to the treatment of artificial viscosity (see Cullen & Dehnen 2010), SPH smoothing kernel accuracy (Dehnen & Aly 2012), and timestep communication relevant for treating extremely high Mach-number shocks (Saitoh & Makino 2009; Durier & Dalla Vecchia…”