### Development of a Polygon Wall Boundary Model Considering Corner of Wall and Its Numerical Application to FSI

Abstract

Fluidâ€“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 and
structure 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 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 since wall 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 and introduce the improved ERP model to stabilized Incompressible
Smoothed Particle Hydrodynamics (ISPH) method. 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 a corner is modified using approximate polynomial based on geometric
property of corner such as angle. 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 of pressure
than the previous one. And according to results of the dam break problem,
it is confirmed that the solution obtained by the improved ERP model is
in better agreement with the experimental result than the previous ERP
model. Also, we conduct some FSI simulations, for example, a dam break
problem with an elastic obstacle and so on.

PDF file