Computational Eulerian hydrodynamics and Galilean invariance

Robertson, Brant; Kravtsov, Andrey V.; Gnedin, Nickolay Y.; Abel, Tom; Rudd, Douglas H.

doi:10.1111/j.1365-2966.2009.15823.x

Cited by 91 publications

(115 citation statements)

References 59 publications

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“…An L1 error norm for the KH problem has been introduced by Robertson et al (2010) and, in analogy with their Equation 11, we conjecture here for L1 a generic dependence of the form…”

Section: 1)mentioning

confidence: 68%

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Improved Performances in Subsonic Flows of an SPH Scheme With Gradients Estimated Using an Integral Approach

Valdarnini

2016

ApJ

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In this paper we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics.In particular we consider the Gresho-Chan vortex problem, the growth of Kelvin-Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disc problem. We compare simulation results for the different tests with those obtained, for the same initial conditions, using standard SPH. We also compare the results with the corresponding ones obtained previously with other numerical methods, such as codes based on a moving-mesh scheme or Godunov-type Lagrangian meshless methods.We quantify code performances by introducing error norms and spectral properties of the particle distribution, in a way similar to what was done in other works. We find that the new SPH formulation exhibits strongly reduced gradient errors and outperforms standard SPH in all of the tests considered. In fact, in terms of accuracy we find good agreement between the simulation results of the new scheme and those produced using other recently proposed numerical schemes. These findings suggest that the proposed method can be successfully applied for many astrophysical problems in which the presence of subsonic flows previously limited the use of SPH, with the new scheme now being competitive in these regimes with other numerical methods.

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“…An L1 error norm for the KH problem has been introduced by Robertson et al (2010) and, in analogy with their Equation 11, we conjecture here for L1 a generic dependence of the form…”

Section: 1)mentioning

confidence: 68%

“…The simulations of Robertson et al (2010) were performed using the Eulerian mesh code ART (Kravtsov et al 1997); note however that their initial condition setup corresponds here to The ratio between the error norms of two different KH runs is then…”

Section: 1)mentioning

confidence: 99%

Improved Performances in Subsonic Flows of an SPH Scheme With Gradients Estimated Using an Integral Approach

Valdarnini

2016

ApJ

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“…This creates a finite shearing layer between the slab and the background, with a width of ∼ 3σ for 95% convergence, which suppresses the growth of perturbations with wavelengths comparable to or smaller than the shearing layer (Robertson et al 2010). In order to effectively suppress the grid noise we find that we require σ > 2∆, where ∆ is the cell size.…”

Section: Methodsmentioning

confidence: 99%

Instability of supersonic cold streams feeding galaxies – I. Linear Kelvin–Helmholtz instability with body modes

Mandelker¹,

Padnos²,

Dekel³

et al. 2016

Mon. Not. R. Astron. Soc.

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Massive galaxies at high redshift are predicted to be fed from the cosmic web by narrow, dense streams of cold gas that penetrate through the hot medium encompassed by a stable shock near the virial radius of the dark-matter halo. Our long-term goal is to explore the heating and dissipation rate of the streams and their fragmentation and possible breakup, in order to understand how galaxies are fed, and how this affects their star-formation rate and morphology. We present here the first step, where we analyze the linear Kelvin-Helmholtz instability (KHI) of a cold, dense slab or cylinder in 3D flowing supersonically through a hot, dilute medium. The current analysis is limited to the adiabatic case with no gravity. By analytically solving the linear dispersion relation, we find a transition from a dominance of the familiar rapidly growing surface modes in the subsonic regime to more slowly growing body modes in the supersonic regime. The system is parametrized by three parameters: the density contrast between stream and medium, the Mach number of stream velocity with respect to the medium, and the stream width with respect to the halo virial radius. A realistic choice for these parameters places the streams near the mode transition, with the KHI exponential-growth time in the range 0.01-10 virial crossing times for a perturbation wavelength comparable to the stream width. We confirm our analytic predictions with idealized hydrodynamical simulations. Our linear estimates thus indicate that KHI may be effective in the evolution of streams before they reach the galaxy. More definite conclusions await the extension of the analysis to the nonlinear regime and the inclusion of cooling, thermal conduction, the halo potential well, self-gravity and magnetic fields.

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“…The mass of the particles was arranged to obtain the correct density profile following a ramp function Robertson et al (2010). In this way, we smoothed the interface density jump to make it comparable to the SPH resolution using…”

Section: Kelvin-helmholtz Instabilitymentioning

confidence: 99%

Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

Garcı́a-Senz

Cabezón

Escartín

2012

A&A

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Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulate the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. These matrix formulations achieve better interpolations of the physical magnitudes but they are, in general, not fully conservative. The matrix approach to the Euler equations has never been used in astrophysics. Aims. We develop and test a fully conservative SPH scheme based on a tensor formulation that can be applied to simulate astrophysical systems. Methods. In the proposed scheme, derivatives are calculated from an integral expression that leads to a tensor (instead of a vectorial) estimation of gradients and reduces to the standard formulation in the continuum limit. The new formulation improves the interpolation of physical magnitudes, leading to a set of conservative equations that resembles those of standard SPH. The resulting scheme is verified using a variety of well-known tests, all of them simulated in two dimensions. We also discuss an application of the proposed tensor method to astrophysics by simulating the stability of a Sun-like polytrope calculated in three dimensions. Results. The proposed scheme is able to improve the results of standard SPH in the two-dimensional tests, especially in the simulation of subsonic hydrodynamic instabilities. Our results for the stability of the Sun-like polytrope suggest that the new method can be used in astrophysics to carry out three-dimensional calculations with a computational cost that is only slightly higher (i.e. ≤50% for a serial code) than that of a standard SPH formulation. Conclusions. A formalism based on a matrix approach to Euler SPH equations was developed and checked. The new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and probably less prone to undergo the tensile instability. The analysis of several test cases suggest that the method may improve the simulation of both subsonic and supersonic systems. An application of the tensor method to astrophysics is, for the first time, successfully carried out. These encouraging results indicates that more work should be invested in the applications of matrix SPH formulations to astrophysics.

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Computational Eulerian hydrodynamics and Galilean invariance

Cited by 91 publications

References 59 publications

Improved Performances in Subsonic Flows of an SPH Scheme With Gradients Estimated Using an Integral Approach

Improved Performances in Subsonic Flows of an SPH Scheme With Gradients Estimated Using an Integral Approach

Instability of supersonic cold streams feeding galaxies – I. Linear Kelvin–Helmholtz instability with body modes

Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

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