Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

Garcı́a-Senz, Domingo; Cabezón, Rubén M.; Escartín, J. A.

doi:10.1051/0004-6361/201117939

Cited by 65 publications

(104 citation statements)

References 22 publications

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“…14 is consistent with the findings of García-Senz et al (2012), who present a new formulation of SPH in which gradients are estimated using a tensorial approach that conserves both linear and angular momentum. The authors demonstrate that when using this higherorder gradient estimator the interpolation of physical quantities is significantly more accurate than in the standard method.…”

Section: D Rayleigh-taylor Instabilitysupporting

confidence: 89%

“…The formulation of García-Senz et al (2012), which was proposed with the aim of calculating SPH gradients with accuracy as high as possible while keeping the benefits of a Lagrangian formulation, looks in this respect very promising and encourages further investigations along the numerical approach proposed in this paper. These would be particularly relevant in the light of the results of Bauer & Springel (2012), who claim that standard SPH fails to properly model the regime of subsonic turbulence.…”

Section: Discussionmentioning

confidence: 96%

“…8.8), the velocity noise would have suppressed the growth of the instability even for the M 6 run. We note that in their RT test, García-Senz et al (2012) were able to recover the growth of the instability using the same amplitude of the velocity perturbation, δv y = 0.01.…”

Section: D Rayleigh-taylor Instabilitymentioning

confidence: 91%

“…The formulation proposed by García-Senz et al (2012) looks particularly promising in this aspect in overcoming the present SPH difficulties.…”

Section: D Rayleigh-taylor Instabilitymentioning

confidence: 99%

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Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

Valdarnini

2012

A&A

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This paper investigates the hydrodynamic performances of an smoothed particle hydrodynamics (SPH) code incorporating an artificial heat conductivity term in which the adopted signal velocity is applicable when gravity is present. To this end, we analyze results from simulations produced using a suite of standard hydrodynamical test problems. In accordance with previous findings, we show that the performances of SPH in describing the development of Kelvin-Helmholtz instabilities depend strongly on both the consistency of the initial condition set-up and the leading error in the momentum equation due to incomplete kernel sampling. In contrast, the presence of artificial conductivity does not significantly affect the results. An error and stability analysis shows that the quartic B-spline kernel (M 5 ) possesses very good stability properties and so we propose its use with a large neighbor number, between ∼50 (2D) to ∼100 (3D), to improve convergence in simulation results without being affected by the so-called clumping instability. Moreover, the results of the Sod shock tube demonstrate that to obtain simulation profiles in accord with the analytic solution, for simulations employing kernels with a non-zero first derivative at the origin, it is necessary to use a much larger number of neighbors than in the case of the M 5 runs. Our SPH simulations of the blob test show that in order to achieve blob disruption it is necessary to include an artificial conductivity term. However, we find that in the regime of strong supersonic flows an appropriate limiting condition, which depends on the Prandtl number, must be imposed on the artificial conductivity SPH coefficients in order to avoid an unphysical amount of heat diffusion. Our results from hydrodynamic simulations that include self-gravity show profiles of hydrodynamic variables that are in much better agreement with those produced using mesh-based codes. In particular, the final levels of core entropies in cosmological simulations of galaxy clusters are consistent with those found using AMR codes. This demonstrates that the proposed diffusion scheme is capable of mimicking the process of entropy mixing that is produced during structure formation because of the diffusion caused by turbulence. Finally, the results of our Rayleigh-Taylor instability test demonstrate that in the regime of very subsonic flows the code still has several difficulties in the treatment of hydrodynamic instabilities. These problems are intrinsic to the way in which standard SPH gradients are calculated and not to the implementation of the artificial conductivity term. To overcome these difficulties, several numerical schemes have been proposed that, if coupled with the SPH implementation presented in this paper, could solve the issues that have recently been addressed in investigating SPH performances to model subsonic turbulence.

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Section: D Rayleigh-taylor Instabilitysupporting

confidence: 89%

Section: Discussionmentioning

confidence: 96%

Section: D Rayleigh-taylor Instabilitymentioning

confidence: 91%

“…The formulation proposed by García-Senz et al (2012) looks particularly promising in this aspect in overcoming the present SPH difficulties.…”

Section: D Rayleigh-taylor Instabilitymentioning

confidence: 99%

See 2 more Smart Citations

Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

Valdarnini

2012

A&A

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“…The resulting tensor scheme has been tested in a variety of hydrodynamical test cases (García-Senz et al 2012;Rosswog 2015), showing significant improvements as compared with the standard formulation. A crucial feature of the method is that it retains the Lagrangian nature of SPH, unlike previous attempts aimed at improving gradient accuracy.…”

Section: Introductionmentioning

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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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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A multimass correction for multicomponent fluid flow simulation using smoothed particle hydrodynamics

Kumar

Patnaik

2018

Numerical Meth Engineering

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In multicomponent fluid flow simulations using smoothed particle hydrodynamics, the Lagrangian particles used are mostly of equal mass. This is preferred over multimass particle setup (particles with different values of mass), as it resolves the fluid interfaces comparatively better. But the flip side of using uniform mass particle setup is that it may not be computationally economical in situations with large-density ratios. Hence, using multimass particle setup is both economical and perhaps inevitable. An attractive feature of multimass particle setup is that it allows uniform resolution in regions with different values of density. To take advantage of the multimass setup, it is therefore imperative to reduce the error associated with its usage. In this work, we present suitable multimass correction terms and assess its effectiveness using the ∇h-smooth particle hydrodynamics scheme. Standard benchmark problems, viz, shock tube test, triple-point shock test, Rayleigh-Taylor instability, and Kelvin-Helmholtz instability were solved with multimass particle setup, where significant improvements could be achieved in resolving the associated contact discontinuities.

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Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

Cited by 65 publications

References 22 publications

Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

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

A multimass correction for multicomponent fluid flow simulation using smoothed particle hydrodynamics

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