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A Corrected Incompressible SPH (CISPH) method is proposed for accurate tracking of water surface in breaking waves. Corrective terms are derived based on a variational approach to ensure the angular momentum preservation of Incompressible SPH (ISPH) formulations. The proposed CISPH method is applied to solve the Navier-Stokes equation for simulating the breaking and post-breaking of solitary waves on a plane slope. The enhanced precision (compared to the ISPH method) of the CISPH method is confirmed through both qualitative and quantitative comparisons with experimental data. The introduction of corrective terms significantly improves the capability and the accuracy of the ISPH method in the simulation of wave breaking and post-breaking.

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a b s t r a c tA new criterion is proposed for a more efficient assessment of free-surface particles in a particlebased simulation. Enhanced wave impact simulations are carried out by improved Incompressible SPH (ISPH) methods. The first improvement is the same as that in the Corrected ISPH (CISPH; [Khayyer A, Gotoh, H, Shao SD. Corrected incompressible SPH method for accurate water-surface tracking in breaking waves, Coast Eng 2008; 55 (3): 236-250]) method and is proposed for the improvement of momentum conservation. The second improvement is achieved by deriving and employing a higher order source term based on a more accurate differentiation to obtain a less fluctuating and more accurate pressure field. The enhanced performance of improved ISPH methods is demonstrated through the simulation of several fluid impact simulations in comparison with the experimental data and simulation results by other numerical methods.

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SUMMARY This paper presents an incompressible SPH (ISPH) technique to simulate multifluid flows. The SPH method is a mesh‐free particle modeling approach that can treat free surfaces and multi‐interfaces in a simple and efficient manner. The ISPH method employs an incompressible hydrodynamic formulation to solve the fluid pressure that ensures a stable pressure field. Two multifluid ISPH models are proposed following different interface treatments: the coupled ISPH model does not distinguish the different fluid phases and applies the standard ISPH technique across the interface, whereas the decoupled ISPH model first treats each fluid phase separately and then couples the different phases by applying pressure and shear stress continuities across the interface. The two proposed models were used to investigate a gravity underflow with a low density ratio in a Generalized Reservoir Hydrodynamics (GRH) flume and a horizontal lock exchange flow with a high density ratio. Comparisons with data and relevant numerical error analysis indicated that the decoupled model performed well in cases of both low and high density ratios because of the accurate treatment of interface boundaries. Copyright © 2011 John Wiley & Sons, Ltd.