Development of a Polygon Wall Boundary Model
Considering Corner of Wall and Its Numerical Application to FSI
Hiroyuki Omura1, Naoto Mitsume2, Mitsuteru Asai3 and Daigoro Isobe41

Graduate School of Science and Technology, University of Tsukuba
1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8573, Japan
E-mail: s2030186@s.tsukuba.ac.jp

2

Division of Engineering Mechanics and Energy, University of Tsukuba
1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8573, Japan
E-mail: mitsume@kz.tsukuba.ac.jp – Web page: https://www.kz.tsukuba.ac.jp/~mitsume/3

Department of Civil Engineering, Kyushu University
744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
E-mail: asai@doc.kyushu-u.ac.jp – Web page: https://kyushu-u.wixsite.com/structural-analysis
4

Division of Engineering Mechanics and Energy, University of Tsukuba
1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8573, Japan
E-mail: isobe@kz.tsukuba.ac.jp – Web page: https://www.kz.tsukuba.ac.jp/~isobe/

ABSTRACT
Fluid–Structure Interaction (FSI) simulation is useful in a wide range of engineering fields.
Especially, the partitioned FSI analysis methods combining a mesh free particle method and a Finite
Element Method (FEM) are in the spotlight. For coupling fluid analysis by particle method andstructure analysis by FEM, transfer of physical variables between fluid domain and structure domain,
namely, wall boundary model for particle method is important. Explicit Represented Polygon (ERP)
wall boundary model [1] is suitable for FSI because of its mechanical and geometrical consistency.
However, the original ERP model has an issue on calculation accuracy near corners of wall sincewall is assumed to be completely plane. Therefore, it cannot be applied to semi-implicit particle
method due to the local error near corners.
In this research, we develop an improved ERP wall boundary model by considering the corners andintroduce the improved ERP model to stabilized Incompressible Smoothed Particle Hydrodynamics(ISPH) method [2]. To consider corners, we extend a definition of reflecting operation for surface
polygon in the original ERP model to corners. Besides, volume of a wall domain expressed for acorner is modified using approximate polynomial based on geometric property of corner such asangle. Finally, we apply the ISPH method with the improved ERP model to partitioned FSI analysis
method.
As verification and validation, we solve hydrostatic pressure problems and a dam break problem
using the stabilized ISPH code with the improved ERP model. Results of the hydrostatic pressure
problem show that the improved ERP model can obtain more smoothed and correct distribution ofpressure than the previous one. And according to results of the dam break problem, it is confirmedthat the solution obtained by the improved ERP model is in better agreement with the experimental
result [3] than the previous ERP model. Also, we conduct some FSI simulations, for example, a dam
break problem with an elastic obstacle and so on.

REFERENCES[1] N. Mitsume et al., “Explicitly Represented Polygon Wall Boundary Model for the Explicit MPS
Method”, Computational Particle Mechanics, 2-1, 73–89 (2015).
[2] M. Asai et al., “A Stabilized Incompressible SPH Method by Relaxing the Density Invariance
Condition”, Journal of Applied Mathematics, 2012, Article ID 139583 (2012).
[3] L. Lobovsky et al., “Experimental Investigation of Dynamic Pressure Loads during Dam Break”,
Journal of Fluids and Structures, 48, 407–434 (2014).