Recently we have developed an improved Smoothed Particle Hydrodynamic (SPH) method for modeling breaking waves. The main features of the method include solving higher order equations to find interpolation of unknown functions and their gradients, and with a new proposed scheme to identify free surface particles. In addition, the newly improved method is applied to sloshing breaking waves, and produces more reasonable pressure distribution and smoother pressure time history.
Many meshless methods have been reported in the literatures, such as Smoothed Particle Hydrodynamics method(SPH)(Monaghan, 1988), Element Free Galerkin method(Belytschko, 1994), Reproducing Kernel Particle Method(RKPM) (Liu, 1995), Moving Particle Semi-implicit method(MPS) (Koshizuka, 1996), Meshless Local Petrov-Galerkin method(MLPG) (Atluri,1998; Ma, 2005), Finite Point Method(Onate, 1996; Fang, 2008), Finite Particle Method(Liu, 2005; Fang, 2009) and so on. Since their invention, they have been extended to solving various problems, such as the dynamic response of elastic-plastic materials(Benz, 1995; Libersky, 1993), breaking waves (Monaghan, 1994), solid friction(Cummins, 1999), incompressible fluids(Lo Edmond, 2002; Shao, 2003, 2006, 2009), multi-phase flows(Monaghan,1995; Colagrossi, 2003), viscoelastic flows(Ellero, 2002, 2005; Fang, 2006), underwater explosion(Liu, 2002, 2003a). For more information on the SPH method, we refer readers to the book by Liu and Liu(2003b) and the most recent review of the method by Liu (2010). Although much effort has been made to improve the SPH, it still requires further refinement, such as better methods for more stable pressure, better approaches to lower energy dissipation, and so on. Although there are a number of improved SPH methods to address these issues, such as incompressible SPH(ISPH) (Lo Edmond, 2002; Shao, 2003, 2006, 2009), Finite Particle Method(FPM) (Liu, 2005; Fang, 2009), and Modified SPH(MSPH) (Zhang, 2007, 2008), all of them need a good technique for identifying free surface particles. Inaccurate identification induces unrealistic pressure distribution, which causes instability.