A corrected smooth particle hydrodynamics formulation of the shallow-water equations

By M. Rodriguez-Paz, Javier Bonet. 2005

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Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future (2016, methodology): “Variants of ISPH were proposed by Shao (2006) and Hu and Adams (2007), and applications to ocean engineering were published by Khayyer, Gotoh and Shah (2009) and Khayyer and Gotoh (2009).”
Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments (2010, background): “Rodriguez-Paz and Bonet also developed a corrected smooth particle hydrodynamics formulation of the shallow-water equations [380].”
Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems (2007, unknown): “By smoothing this collection of point masses via a kernel function w(x) a continuous approximation of the density field [18, 19] is obtained as (x) = ∫ ̂(x′)w(x − x′, h) dx′ ∫ w(x′ − x, h) dx (20)”