An improved SPH method: Towards higher order convergence

Oger, G.; Döring, M.; Alessandrini, B.; Ferrant, P.

doi:10.1016/j.jcp.2007.01.039

Cited by 234 publications

(124 citation statements)

References 17 publications

(40 reference statements)

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“…However, the IAD 0 method was unaffected by this problem, hence we found that the tensor method seems to be less susceptible to pairing instability. The ability of matrix methods to cope with pairing instability has been reported by other authors (Oger et al 2007), and they merit further investigation in the context of IAD 0 .…”

Section: Kelvin-helmholtz Instabilitysupporting

confidence: 59%

“…Nevertheless, none of these schemes are able to simultaneously achieve re-normalization, exact momentum and energy conservation, perfect linear interpolation and implicitly include the gradient of the smoothing length in the equations (Oger et al 2007). Nevertheless, IAD 0 is probably the optimal formulation because it fulfills almost all the above requirements with a moderate computational overload.…”

Section: Resultsmentioning

confidence: 99%

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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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Section: Kelvin-helmholtz Instabilitysupporting

confidence: 59%

Section: Resultsmentioning

confidence: 99%

Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

Garcı́a-Senz

Cabezón

Escartín

2012

A&A

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“…To address these pressure oscillations and instabilities in future work, we should refer to current and past methods, such as the least-squares MPS method to reduce serious instabilities including unphysical pressure oscillation 20) . We also could refer to an updated MPS method to reduce the tensile-stress-induced instability 21) , an improved SPH method based on normalization and monitoring of strong conversion states 22) , and an improved SPH method with better moving least-squares interpolants 23) .…”

Section: Resultsmentioning

confidence: 99%

Simulation of Driftwood-induced Flooding during High-intensity Rainfall using Smoothed Particle Hydrodynamics Method

2014

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Worldwide climate change has resulted in severe flooding in Japan in the last decade. Some floods were likely caused by the substantial accumulation of driftwood or debris at bridges crossing rivers in mountainous areas. In this study, for a two-dimensional open channel, we conducted a laboratory experiment and numerical simulation with and without driftwood modeling to clarify the physical mechanism of a flood event resulting from driftwood accumulation at a bridge. Open-source software SPHysics, implementing a smoothed particle hydrodynamics method, was calibrated with data of the water level measured near a miniature bridge in the laboratory experiment. The simulation clearly showed that the particle-like flow was scattered by the bridge girder and dammed up by the bridge in the upstream direction. By changing the quantity of driftwood, we analyzed the effect of a flood on a bridge. For the largest quantity of driftwood, the higher pressure pushing against the bridge may damage the bridge.

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“…the external force. Different approaches [93][94][95] are available to derive the density particle approximation of the continuity, Eq. (15a), and momentum, Eq.…”

Section: Sph Form Of Governing Equationsmentioning

confidence: 99%

Free-Surface Flow Simulations with Smoothed Particle Hydrodynamics Method using High-Performance Computing

Altomare¹,

Viccione²,

Tagliafierro³

et al. 2018

Computational Fluid Dynamics - Basic Instruments and Applications in Science

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Today, the use of modern high-performance computing (HPC) systems, such as clusters equipped with graphics processing units (GPUs), allows solving problems with resolutions unthinkable only a decade ago. The demand for high computational power is certainly an issue when simulating free-surface flows. However, taking the advantage of GPU's parallel computing techniques, simulations involving up to 10 9 particles can be achieved. In this framework, this chapter shows some numerical results of typical coastal engineering problems obtained by means of the GPU-based computing servers maintained at the Environmental Physics Laboratory (EPhysLab) from Vigo University in Ourense (Spain) and the Tier-1 Galileo cluster of the Italian computing centre CINECA. The DualSPHysics free package based on smoothed particle hydrodynamics (SPH) technique was used for the purpose. SPH is a meshless particle method based on Lagrangian formulation by which the fluid domain is discretized as a collection of computing fluid particles. Speedup and efficiency of calculations are studied in terms of the initial interparticle distance and by coupling DualSPHysics with a NLSW wave propagation model. Water free-surface elevation, orbital velocities and wave forces are compared with results from experimental campaigns and theoretical solutions.

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An improved SPH method: Towards higher order convergence

Cited by 234 publications

References 17 publications

Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

Simulation of Driftwood-induced Flooding during High-intensity Rainfall using Smoothed Particle Hydrodynamics Method

Free-Surface Flow Simulations with Smoothed Particle Hydrodynamics Method using High-Performance Computing

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