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A Corrected Moving Particle Semi-implicit (CMPS) method is proposed for the accurate tracking of water surface in breaking waves. The original formulations of standard MPS method are revisited from the view point of momentum conservation. Modifications and corrections are made to ensure the momentum conservation in a particle-based calculation of viscous incompressible free-surface flows. A simple numerical test demonstrates the excellent performance of the CMPS method in exact conservation of linear momentum and significantly enhanced preservation of angular momentum. The CMPS method is applied to the simulation of plunging breaking and post-breaking of solitary waves. Qualitative and quantitative comparisons with the experimental data confirm the high capability and precision of the CMPS method. A tensor-type strain-based viscosity is also proposed to further enhanced CMPS reproduction of a splash-up.

The paper presents a three-dimensional Corrected MPS (3D-CMPS) method for improvement of water surface tracking in breaking waves. The Corrected MPS (CMPS; Khayyer and Gotoh, 2008) has been extended to three dimensions and a 3D-CMPS method has been developed on the basis of the 3D-MPS method by Gotoh et al. (2005b). The improved performance of the 3D-CMPS method with respect to the 3D-MPS method has been shown by simulating a plunging breaking wave and resultant splash-up on a plane slope. Furthermore, the parallelization of 3D-CMPS method with two different solvers of simultaneous linear equations, namely, namely, the PICCG-RP (Parallelized ICCG with Renumbering Process; Iwashita and Shimasaki, 2000) and SCG (Scaled Conjugate Gradient; Jennings and Malik, 1978) techniques, has been performed to enhance the computational efficiency of the calculations. This study also applies a simple dynamic domain decomposition for an optimized load balancing among the processors.