Numerical analysis of breaking waves using the moving particle semi-implicit method

Seiichi Koshizuka*, Atsushi Nobe, Yoshiaki Oka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

774 Citations (Scopus)


The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave.

Original languageEnglish
Pages (from-to)751-769
Number of pages19
JournalInternational Journal for Numerical Methods in Fluids
Issue number7
Publication statusPublished - 1998 Apr 15
Externally publishedYes


  • Breaking wave
  • Free surface
  • Incompressible flow
  • MPS
  • Particle method
  • Surf similarity parameter

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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