An improved SPH method: Towards higher order convergence

By Guillaume Oger, Mathieu Doring, Bertrand Alessandrini, Pierre Ferrant. Journal of Computational Physics, 2007

320 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2d58723f411157682d08248484d59934f3ed290e

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Smoothed Particle Hydrodynamics in Astrophysics (2010, background): “Finally, a higher order formulation of SPH has also been proposed (Oger et al., 2007).”
Corrected First-Order Derivative ISPH in Water Wave Simulations (2017, methodology): “The second one was introduced by using the corrections of kernel gradient (Bonet and Lok, 1999; Oger et al., 2007), which ensured the SPH pressure gradient term to preserve both linear and angular momentums.”
Comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in ISPH context (2017, background): “These gradient models do not provide anti-symmetric pressure inter-particle forces and thus, do not guarantee local, and global momentum conservation [21,22].”
State-of-the-art of classical SPH for free-surface flows (2010, background): “Strictly speaking, operations that correct the kernel gradient no longer preserve the momentum conserving properties of the SPH method (Vaughan et al. 2008); however, the potential gain in accuracy and stability means that these techniques still possess unique attractions (Oger et al. 2007).”
Enhancement of stability and accuracy of the moving particle semi-implicit method (2011, background): “A more accurate approximation of pressure gradient can be achieved by focusing on the Taylor series expansion of pressure at a neighbouring particle j with respect to the pressure at a target particle i (as shown by [10,58]).”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, methodology): “…terms to restore the completeness or consistency (Colagrossi et al. 2011) of formulations (e.g. Randles andLibersky 1996;Chen et al. 1999; Oger et al. 2007; Schwaiger 2008; Fatehi and Manzari 2011a; Jiang et al. 2012) as well as momentum conservation (e.g. Bonet and Lok 1999; Hopkins…”
Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves (2012, background): “Gradient and divergence operator Unless otherwise stated, the gradient operator for a general variable / is given by $/i ’ X j V jð/i /jÞrxij: ð5Þ This choice of gradient operator is preferred over others due to its increased accuracy when used in combination with the kernel gradient normalisation [”