SPH accuracy improvement through the combination of a quasi-Lagrangian shifting transport velocity and consistent ALE formalisms

Oger, G.; Marrone, S.; Touzé, David Le; Leffe, M. de

doi:10.1016/j.jcp.2016.02.039

Cited by 169 publications

(108 citation statements)

References 44 publications

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“…In fact, Lagrangian particle methods probably become unstable when accurate formulations are directly adopted, owing to the following facts: particle distribution distortion takes place easily when particles precisely move along streamlines, as shown in the work of Matsunaga et al (see fig. 9 therein) or Oger et al (see fig. 1 therein).…”

Section: Introductionmentioning

confidence: 92%

An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models

Duan

Koshizuka

Yamaji

et al. 2018

Numerical Meth Engineering

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Summary The Lagrangian moving particle semi‐implicit (MPS) method has potential to simulate free‐surface and multiphase flows. However, the chaotic distribution of particles can decrease accuracy and reliability in the conventional MPS method. In this study, a new Laplacian model is proposed by removing the errors associated with first‐order partial derivatives based on a corrected matrix. Therefore, a corrective matrix is applied to all the MPS discretization models to enhance computational accuracy. Then, the developed corrected models are coupled into our previous multiphase MPS methods. Separate stabilizing strategies are developed for internal and free‐surface particles. Specifically, particle shifting is applied to internal particles. Meanwhile, a conservative pressure gradient model and a modified optimized particle shifting scheme are applied to free‐surface particles to produce the required adjustments in surface normal and tangent directions, respectively. The simulations of a multifluid pressure oscillation flow and a bubble rising flow demonstrate the accuracy improvements of the corrective matrix. The elliptical drop deformation demonstrates the stability/accuracy improvement of the present stabilizing strategies at free surface. Finally, a turbulent multiphase flow with complicated interface fragmentation and coalescence is simulated to demonstrate the capability of the developed method.

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Section: Introductionmentioning

confidence: 92%

An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models

Duan

Koshizuka

Yamaji

et al. 2018

Numerical Meth Engineering

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“…Generally, the maximum convection distance U max Δt is appropriate for evaluating the magnitude of shifting vector. In fact, the maximum convection distance herein used is similar to the characteristic velocity of the flow considered in ALE‐SPH . In addition, Lind et al pointed out that the artificial pressure‐like function 0.2[ W / W (Δ)] 4 described by Monaghan can mitigate the tensile instability.…”

Section: Particle Shifting Technologymentioning

confidence: 99%

“…In a genuine ALE framework proposed by Vila, Oger et al introduced a specific transport velocity to avoid the appearance of anisotropic particle structures. For ALE‐SPH, the most critical factor is how to impose a disordering transport velocity to avoid disorder particle distributions and maintain high accuracy and stability.…”

Section: Introductionmentioning

confidence: 99%

Coupled finite particle method with a modified particle shifting technology

Huang

Zhang

Shi

et al. 2017

Numerical Meth Engineering

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Summary The conventional SPH method has been frustrated with the low accuracy originated from the particle inconsistency. The finite particle method (FPM) is an improved SPH method with a higher‐order accuracy. However, the numerical accuracy and stability of FPM depend on the uniformity of particles. Facing the disorder particles, the conventional FPM may suffer from an ill‐conditioned corrective matrix and is difficult to conduct longtime simulations. A popular and robust particle regularization scheme is the so‐called particle shifting technology (PST), which can effectively enhance the accuracy and stability of particle methods. In the context of FPM, PST is analyzed and discussed, and a modified PST (MPST) is proposed. Modified PST saves great amount of computational cost with respect to the conventional PST and acquires better features of accuracy and stability. Finally, the coupled FPM method by combining MPST and δ‐SPH is developed to simulate a series of viscous flows. The numerical results indicate that MPST is effective in improving accuracy, stability, and efficiency of PST, and the coupled FPM is shown to be robust for simulating viscous flows and has a higher accuracy and stability.

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“…Gotoh and Khayyer and Violeau and Rogers have addressed several other improvements regarding the accuracy of SPH methods. In an accurate model, however, particles tend to follow more accurately the flow trajectories in the Lagrangian coordinate, leading to an irregular particle distribution as discussed by Oger et al Concerning particle interactions, each particle in the SPH method interacts with its adjacent particles through a symmetric kernel function; therefore, any irregular distribution of particles may introduce numerical errors in spatial differential operators. As a good case in point, particle clamping and probable tensile instabilities are some other defects of particle disarrangements.…”

Section: Introductionmentioning

confidence: 99%

An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

Akbari

2019

Numerical Methods in Fluids

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Summary The smoothed particle hydrodynamics (SPH) method is one of the powerful Lagrangian tools for modeling free surface flows. However, it suffers from particle disorder, which leads to interpolation and numerical errors. To overcome this problem, several techniques have been introduced until now, among which the particle shifting technique (PST) based on Fick's law is an efficient one. The current form of this method needs tuning parameters to fulfill numerical stability criteria. In this study, to eliminate calibration factors, a new shifting coefficient is derived theoretically based on particle positions before and after shifting, regardless of other parameters such as velocity, pressure, time step intervals, etc. The only required input is particle positions, and the main concern is conserving particle densities in their updated positions. In addition to the proposed PST, a new distribution index (DI) is introduced for measuring the spatial uniformity of particles. Furthering the research, some novel treatments are also studied to improve particle movements near free surface boundary. The proposed idea is only assessed for ISPH method in this study, and its performance in other SPH schemes needs more investigations. Following this innovative method, it is validated by modeling different cases including dam break flow, paddle movement, and elliptical water drop. In all cases, particle arrangements have been improved by means of the modified shifting method. In that sense, good agreements between simulation results with experimental data, analytical solutions, and other numerical methods approve the ability of the developed method in simulating free surface flows.

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SPH accuracy improvement through the combination of a quasi-Lagrangian shifting transport velocity and consistent ALE formalisms

Cited by 169 publications

References 44 publications

An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models

An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models

Coupled finite particle method with a modified particle shifting technology

An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

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