Smoothed particle hydrodynamics and magnetohydrodynamics

By Daniel J. Price. Journal of Computational Physics, 2010

652 citations recorded by the source corpus.

This paper presents an overview and introduction to smoothed particle hydrodynamics and magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several 'urban myths' regarding SPH, in particular the idea that one can simply increase the 'neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the ndspmhd SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/b660bf88fc7b6f970ff3c263675a63bc285c6de7

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Citations in the corpus

Thin-film smoothed particle hydrodynamics fluid (2021, neutral): “It can also be extended to different applications such as simulating multiphase flow, computing magnetohydrodynamics, and blue noise sampling [Jiang et al. 2015; Price 2012; Tartakovsky and Meakin 2005].”
An improved SPH scheme for cosmological simulations (2015, methodology): “However, the standard weighting functions of SPH respond differently to an increase of smoothing neighbours and can possibly become unstable to the pairing instability (Schuessler & Schmitt 1981; Price 2012a).”
Lagrangian Fluid Simulation with Continuous Convolutions (2020, background): “Among others, it has been highly successful for modeling interface ﬂows (Colagrossi & Landrini, 2003), complex multi-phase phenomena (Hu & Adams, 2006), and even magnetohydrodynamics (Price, 2012).”
Galaxies on FIRE (Feedback In Realistic Environments): stellar feedback explains cosmologically inefficient star formation (2013, background): “For more discussion see Price (2012). adaptive (following the approximate “fixed mass in kernel” prescription in Springel & Hernquist 2002), enclosing ∼ 64 neighbors.”
Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves (2012, background): “As reiterated by Price [22], in weakly compressible SPH the conservative pressure gradient term is often more beneficial than the non-conservative form, as it automatically self-regulates particles.”
Tearing up the disc: misaligned accretion on to a binary (2013, methodology): “We use the smoothed particle hydrodynamics (SPH; e.g. Price 2012) code PHANTOM (see e.g. Lodato & Price 2010; Price & Federrath 2010; Nixon 2012; Nixon et al. 2012a) to simulate the evolution of circumbinary discs.”
Neutrino-driven winds from neutron star merger remnants (2014, methodology): “For overviews over the SPH method, the interested reader is referred to recent reviews (Monaghan 2005; Rosswog 2009, 2014a,b; Springel 2010; Price 2012).”
On planet formation in HL Tau (2015, methodology): “We perform 3D global simulations of dust/gas discs with embedded protoplanets using thePHANTOM smoothed particle hydrodynamics (SPH) code written by DP (rice & Federrath 2010; Lodato & Price 2010; Price 2012; Nixon, King & Price 2013).”
The EAGLE simulations of galaxy formation: the importance of the hydrodynamics scheme (2015, methodology): “In the case of simulations using Smoothed Particle Hydrodynamics (SPH) solvers (Lucy 1977; Gingold & Monaghan 1977) (see Springel 2010a; Price 2012, for reviews), the free parameters relate to the treatment of shocks, artificial viscosity and conduction and are related to the way the SPH equations…”
Fluid–particle flow simulations using two-way-coupled mesoscale SPH–DEM and validation (2013, methodology): “The rate of change of superficial density is calculated using the variable smoothing length terms derived by Price (2012).”
Improving convergence in smoothed particle hydrodynamics simulations without pairing instability (2012, methodology): “This type of noise is a well-known issue with multidimensional SPH simulations of shocks (e.g. Springel 2010; Price 2012).”
Gasoline2: a modern smoothed particle hydrodynamics code (2017, methodology): “We refer the reader to recent reviews of SPH for additional perspectives, such as Springel (2010a); Price (2012a); and Rosswog (2015).”
A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems (2012, methodology): “So with identical artificial viscosity, the Price (2012a) result is identical to ours over the inertial range (including the initial “drop off”).”
Moving mesh cosmology: numerical techniques and global statistics (2011, neutral): “…circumventing this problem and allowing a higher neighbour number require different kernel shapes than are commonly employed (Read et al. 2010; Price 2012), but such kernels merely have different stability bands that still impose severe restrictions on the number of neighbours that may be…”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, methodology): “There has been considerable effort to “fix” SPH, and FIRE-1 used the improved P-SPH methods from Saitoh & Makino (2013) and Hopkins (2013a) to reduce these errors, but some (e.g. the zeroth-order errors) cannot be entirely eliminated in SPH without de-stabilizing the method (see Price 2012).”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, background): “As shown by Price (2012a) and Hopkins (2013), an artificial viscosity switch improves the performance of SPH greatly, and even allows us to see some convergence, but at all resolutions we study the cascade in PSPH is still truncated compared to the non-SPH methods (by a factor ∼ 4).”
Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future (2016, methodology): “In the 1980s, while continuing its development in astrophysics and magnetohydrodynamics (see a recent review by Price, 2012), SPH was successfully applied to elasticity and fracturing processes (e.g. Campbell, Vignjevic, & Libersky, 2000).”