Journal of Hydrodynamics

, Volume 30, Issue 6, pp 1120–1133 | Cite as

Water entry of decelerating spheres simulations using improved ISPH method

  • Abdelraheem M. AlyEmail author
  • Mitsuteru Asai


In this paper, we simulated the vertical impact of spheres on a water surface using three-dimensional incompressible smoothed particle hydrodynamics (3-D ISPH) method. The sphere motion is taken to be a rigid body motion and it is modeled by ISPH method. The governing equations are discretized and solved numerically using ISPH method. A stabilized incompressible SPH method by relaxing the density invariance condition is adopted. Here, we computed the motions of a rigid body by direct integration of the fluid pressure at the position of each particle on the body surface. The equations of translational and rotational motions were integrated in time domain to update the position of the rigid body at each time step. In this study, we improved the boundary treatment between fluid and fixed solid boundary by using virtual marker technique. In addition, an improved algorithm based on the virtual marker technique for the boundary particles is proposed to treat the moving boundary of the rigid body motion. The force exerted on the moving rigid boundary particles by the surrounding particles, is calculated by the SPH approximation at the virtual marker points. The applicability and efficiency of the current ISPH method are tested by comparison with reference experimental results.

Key words

Incompressible smoothed particle hydrodynamics (ISPH) free surface flow sphere rigid body water entry 


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The first author (A. M. Aly) would like to express his gratitude to King Khalid University, Saudi Arabia for providing administrative and technical support.


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Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Khalid UniversityAbhaSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceSouth Valley UniversityQenaEgypt
  3. 3.Department of Civil EngineeringKyushu UniversityFukuokaJapan

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