Particle method, which is a solver of Navier-Stokes equation without using a computational grid, has excellent robustness in analyzing a violent water-surface change accompanied with a fragmentation and a coalescence of water. Therefore the particle method is an optimum tool for the analysis of the process of wave breaking and runup. Herein, calculation fundamentals of the particle method are outlined. The stateof- the-art of the particle method, including highly-precise particle methods by improving momentum conservation in discretization of governing equations and the new methods for a control of pressure fluctuation, is briefly introduced. Finally few of significant issues for promoting substantial contribution of the particle method to numerical wave flume, which is the computer-aided resistive design tool of coastal structures against wave action, are shown as prospective studies on the particle method.
To describe nonlinear wave transformation, the Boussinesq(1872) theory and its extension (e.g. Nwogu, 1993) are popular and reliable. However these models are unable to describe wave breaking directly, because these models are derived under the assumption of potential flow, namely irrotational flow with neglecting viscosity. In extended models of the Boussinesq theory, wave breaking was described empirically as an energy damping effect with using ad-hoc energy dissipating schemes (e.g. Svendsen, 1984). Computations based on analytical governing equations of wave motion, such as Boussinesq equation, must be replaced by numerical solutions of Navier-Stokes equation to analyze a wave breaking and a runup process without ad-hoc sub-models of energy dissipation. In the wave breaking phenomena, there exist one more difficulty, namely existence of multiply connected flow domain, or topological change of free surface, due to plunging jet striking the toe of the wave. Under this condition, Lagrangian grid methods, which track a free surface with using moving grid, break down. The Maker-And-Cell (MAC) method (Harlow and Welch, 1965), which captured water surface by tracking markers existing in the vicinity of water surface, was the first computational approach to overcome this difficulty.
