A DENSITY-INDEPENDENT FORMULATION OF SMOOTHED PARTICLE HYDRODYNAMICS

By Takayuki R. Saitoh, J. Makino. 2012

144 citations recorded by the source corpus.

The standard formulation of the smoothed particle hydrodynamics (SPH) assumes that the local density distribution is differentiable. This assumption is used to derive the spatial derivatives of other quantities. However, this assumption breaks down at the contact discontinuity. At the contact discontinuity, the density of the low-density side is overestimated while that of the high-density side is underestimated. As a result, the pressure of the low-density (high-density) side is overestimated (underestimated). Thus, unphysical repulsive force appears at the contact discontinuity, resulting in the effective surface tension. This tension suppresses fluid instabilities. In this paper, we present a new formulation of SPH, which does not require the differentiability of density. Instead of the mass density, we adopt the internal energy density (pressure) and its arbitrary function, which are smoothed quantities at the contact discontinuity, as the volume element used for the kernel integration. We call this new formulation density-independent SPH (DISPH). It handles the contact discontinuity without numerical problems. The results of standard tests such as the shock tube, Kelvin–Helmholtz and Rayleigh–Taylor instabilities, point-like explosion, and blob tests are all very favorable to DISPH. We conclude that DISPH solved most of the known difficulties of the standard SPH, without introducing additional numerical diffusion or breaking the exact force symmetry or energy conservation. Our new SPH includes the formulation proposed by Ritchie & Thomas as a special case. Our formulation can be extended to handle a non-ideal gas easily.

Subfields: Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/dcf5b368a7e794b2568b3fc183137a5b57cde8f2

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Citations in the corpus

The cosmic baryon cycle and galaxy mass assembly in the FIRE simulations (2016, methodology): “All simulations are run using the “P-SPH" mode of the GIZMO simulation code2 (Hopkins 2015), employing a pressure-entropy formulation of SPH that minimizes some of the major problems previous formulations of SPH have with fluid mixing instabilities (Hopkins 2013; Saitoh & Makino 2013).”
Galaxies on FIRE (Feedback In Realistic Environments): stellar feedback explains cosmologically inefficient star formation (2013, background): “…“surface tension” error term which appears at contact discontinuities in previous (“density-energy” or “densityentropy”) formulations of SPH (see also Saitoh & Makino 2013).30 The pressure-entropy formulation dramatically improves the behavior of fluid mixing instabilities (e.g. the…”
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).”
The impact of baryonic physics on the structure of dark matter haloes: the view from the FIRE cosmological simulations (2015, background): “P-SPH eliminates artificial surface tension at contact discontinuities that affects traditional density based SPH (Agertz et al. 2007; Saitoh & Makino 2013; Sijacki et al. 2012).”
The neutral hydrogen content of galaxies in cosmological hydrodynamic simulations (2013, methodology): “In future work we plan to investigate the detailed dynamical processes that remove the H i from satellites in our simulations, though this will likely require some modification to the hydrodynamics algorithm (Agertz et al. 2007; Read & Hayfield 2012; Saitoh & Makino 2013).”
The Auriga Project: the properties and formation mechanisms of disc galaxies across cosmic time (2016, methodology): “Recent modifications to the standard SPH method, such as pressure-based SPH (Read, Hayfield & Agertz 2010; Saitoh & Makino 2013) and the inclusion of artificial thermal conductivity, have improved the situation somewhat, particularly with regard to the mixing and hydrodynamical instabilities…”
An improved SPH scheme for cosmological simulations (2015, methodology): “Lately, AC (see e.g. Price 2008) or pressure–entropy formulations (Hopkins 2013; Saitoh & Makino 2013) were proposed to overcome these issues.”
Neutral hydrogen in galaxy haloes at the peak of the cosmic star formation history (2014, background): “…found in traditional density-based SPH formulations (e.g., Agertz et al. 2007) and resolves the major historical differences between SPH and grid-based codes (included adaptive and moving mesh methods), particularly with respect to fluid mixing instabilities (see also Saitoh & Makino 2013).”
Physical Models of Galaxy Formation in a Cosmological Framework (2014, methodology): “A different approach was pursued by Saitoh & Makino (2013), following on Ritchie & Thomas (2001).”
The EAGLE project: Simulating the evolution and assembly of galaxies and their environments (2014, methodology): “As described in more detail below, we employ the fully conservative SPH formulation derived by Hopkins (2013), of which the solutions suggested by Ritchie & Thomas (2001), Read et al. (2010) and Saitoh & Makino (2013) are special cases.”
Gravitational torque-driven black hole growth and feedback in cosmological simulations (2016, unknown): “…0.16 105 0.5 103 20 0 Large momentum boost 600 3.3e-2 n256-nf 6.4e6 0.16 105 0.5 0 0 0 No feedback 0 0 n256-mfm 6.4e6 0.16 105 0.5 103 1 0 Meshless hydrodynamics 30 1.6e-3 n512 8.0e5 0.08 105 0.5 103 1 2 High resolution 30 1.6e-3 fluid mixing instabilities (Hopkins 2013; Saitoh & Makino 2013).”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “• “Modern” SPH (PSPH): This refers to “modern” SPH formulations described in § 1 and § F2.”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, methodology): “(iii) Energy density-based smoothing: Saitoh and Makino (2013) developed an alternative SPH model which incorporates energy density, rather than mass density, as the basis for smoothing. By utilizing this approach, density differentiability is no longer a prerequisite and hence contact discontinuiti”
The EAGLE simulations of galaxy formation: the importance of the hydrodynamics scheme (2015, methodology): “(10) The use of the smoothed quantities P̄i and ρ̄i in the equations of motion smooths out the spurious pressure jumps appearing at contact discontinuities in older formulations of SPH (Saitoh & Makino 2013; Hopkins 2013).”
Gasoline2: a modern smoothed particle hydrodynamics code (2017, methodology): “This test is used to demonstrate the presence of surface tensionlike effects (Hopkins 2013; Saitoh & Makino 2013; Hu et al. 2014; Hopkins 2015).”