An approach for tension instability in smoothed particle hydrodynamics (SPH)

Dyka, C. T.; Ingel, R. P.

doi:10.1016/0045-7949(95)00059-p

Cited by 210 publications

(124 citation statements)

References 3 publications

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“…Randles and Libersky [111] proposed adding dissipative terms, which is relate to conservative smoothing. Dyka [127] proposed an original solution by using a noncollocated discretisation of stress and velocity points. At one set of points, the stresses are evaluate, while the momentum equation is calculated at another set of points.…”

Section: Tensile Instabilitymentioning

confidence: 99%

See 1 more Smart Citation

Brief Review of Numerical Simulation Applied to Solve Oil Extraction Problems

Onofre-Ramos¹,

Castañeda²,

Austria-Aguilar³

et al. 2015

IJG

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In the last decades, the numerical analysis has abridged the time and cost of oil extractive operations, and thus their implementation has been promoted so much that today is used to solve a large number of phenomena that occur during the extraction of hydrocarbons, not only economizing the operation, but also shedding light to the phenomenon, and helping to have a better understanding. Nevertheless in spite of the success of the applications of numerical simulations, it has been until today, looking for their optimization, because the discretization methods of the domain and the model are through meshes, which require modifying the physics of the problem so that this matches the numerical method, and not in backwards.

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Section: Tensile Instabilitymentioning

confidence: 99%

“…Another unconventional solution to the SPH tensile instability problem was first proposed by Dyka [127] in which the stresses are calculated at the locations other than the SPH particles. The results achieved in 1D were encouraging but a rigorous stability analysis was not performed.…”

Section: Introductionmentioning

confidence: 99%

Brief Review of Numerical Simulation Applied to Solve Oil Extraction Problems

Onofre-Ramos¹,

Castañeda²,

Austria-Aguilar³

et al. 2015

IJG

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“…The concept of 'stress points' was introduced by Dyka et al [27], as an attempt to eliminate tensile instabilities [28] in SPH. The basic idea, which still remains in the stress-point SPH literature, is to 'calculate stresses away from the centroids (particles)'.…”

Section: Stress Pointsmentioning

confidence: 99%

“…However, if Lagrangian kernels are employed the diagram is computed only in the initial configuration, and the method results quite efficient. Finally, we would like to propose another implementation of stress points, which is in some sense a 2D extension of the 1D algorithm by Dyka et al [27], where an 'element' was associated to each SPH particle and stresses computed using two integration (stress) points inside each 'element'. In a 2D version of this approach, certain region is associated to each particle and several representative points within that region are used as quadrature points.…”

Section: Stress Pointsmentioning

confidence: 99%

On the Galerkin formulation of the smoothed particle hydrodynamics method

Cueto‐Felgueroso¹,

Colominas²,

Mosqueira³

et al. 2004

Numerical Meth Engineering

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SUMMARYIn this paper, we propose a Galerkin-based smoothed particle hydrodynamics (SPH) formulation with moving least-squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyse several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena.

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“…The Lagrangian-based method is quite practical when dealing with relatively small particles (such as planets and stars) in a large domain filled with empty space; it is computationally wasteful to model vast sums of empty space with no activity in it. At smaller scales, however, SPAM and SPH suffer from tensile instability [28][29][30][31][32], as particles under tensile stress eventually become unstable regardless of the size of time-integration steps. Efforts to use artificial viscosity approaches have only had limited success [23,26].…”

Section: Introductionmentioning

confidence: 99%

A Discrete Approach to Meshless Lagrangian Solid Modeling

Marko¹

2017

Preprint

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Abstract:The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid-solid interactions.

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An approach for tension instability in smoothed particle hydrodynamics (SPH)

Cited by 210 publications

References 3 publications

Brief Review of Numerical Simulation Applied to Solve Oil Extraction Problems

Brief Review of Numerical Simulation Applied to Solve Oil Extraction Problems

On the Galerkin formulation of the smoothed particle hydrodynamics method

A Discrete Approach to Meshless Lagrangian Solid Modeling

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