We have developed a hybrid method for FSI problem with free surface, named
the MPS-FE method [1, 2]. This method adopts the Moving Particle
Semi-implicit/Simulation (MPS) [3] method, a mesh-free particle method, for free
surface flow computation because of its robustness in long-term analyses with
moving boundaries, and Finite Element Method (FEM) for structure computation
because of its high accuracy and reliability. The method combines the advantages
of both methods and achieves efficiency and robustness. These two methods are
coupled with a partitioned coupling approach, i.e. the conventional serial staggered
(CSS) scheme [4], which can set different time step sizes for the fluid and structure
computations.
The conventional MPS-FE method [1], in which MPS wall boundary particles
and finite elements are overlapped in order to exchange information on
fluid-structure interfaces, has difficulty in dealing with complex shaped
fluid-structure interfaces, because the wall particles have to be set in an orthogonal
and uniform grid manner. In addition, forces on fluid-structure interfaces are not
balanced when the pressure on the walls is calculated in the conventional MPS-FE
method. As the next step, we adopted existing polygon wall boundary models
[5, 6], which can treat a wall boundary as an arbitrary plane, and improved the
MPS-FE methods so that the fluid and structure interfaces are consistent. However,
the existing polygon wall boundary models cannot satisfy the pressure Neumann or
the slip/no-slip boundary conditions, so these cause instability near the boundaries
and deteriorate the accuracy.
In this study, we developed a new polygon wall boundary model for fully
explicit algorithms (Explicit-MPS [7]: E-MPS), called the Explicitly Represented
Polygon (ERP) wall boundary model [8] to compose more accurate MPS-FE
method. The ERP model is formulated such that it satisfies the pressure Neumann
boundary condition and the slip/no-slip boundary condition, without requiring the
generation of virtual particles or treating angled edges as exceptional cases.
Moreover, the ERP model eliminates the problem of force imbalance on the
boundaries, which occurs in conventional models.
2 ERP Wall Boundary Model for Explicit-MPS Method
Regarding the wall boundary treatments, research has made greater progress for the
SPH method [9], which is one of mesh-free particle methods. The repulsive-force
model [10] has been developed in order to avoid penetration of fluid particles across
wall boundaries. Although this model is relatively easy to implement, it causes the
instability of fluid particles near wall boundaries because the boundary conditions
are not satisfied. On the other hand, the ghost (mirror) particle approach [11] is
widely used to satisfy the boundary conditions on walls. In this approach, virtual
particle is generated at reflectional position across the wall of each fluid particle.
These mirror particles are given pressure and velocity values so that the pressure
Neumann boundary condition and slip/no-slip condition are satisfied. However, this
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the MPS-FE method [1, 2]. This method adopts the Moving Particle
Semi-implicit/Simulation (MPS) [3] method, a mesh-free particle method, for free
surface flow computation because of its robustness in long-term analyses with
moving boundaries, and Finite Element Method (FEM) for structure computation
because of its high accuracy and reliability. The method combines the advantages
of both methods and achieves efficiency and robustness. These two methods are
coupled with a partitioned coupling approach, i.e. the conventional serial staggered
(CSS) scheme [4], which can set different time step sizes for the fluid and structure
computations.
The conventional MPS-FE method [1], in which MPS wall boundary particles
and finite elements are overlapped in order to exchange information on
fluid-structure interfaces, has difficulty in dealing with complex shaped
fluid-structure interfaces, because the wall particles have to be set in an orthogonal
and uniform grid manner. In addition, forces on fluid-structure interfaces are not
balanced when the pressure on the walls is calculated in the conventional MPS-FE
method. As the next step, we adopted existing polygon wall boundary models
[5, 6], which can treat a wall boundary as an arbitrary plane, and improved the
MPS-FE methods so that the fluid and structure interfaces are consistent. However,
the existing polygon wall boundary models cannot satisfy the pressure Neumann or
the slip/no-slip boundary conditions, so these cause instability near the boundaries
and deteriorate the accuracy.
In this study, we developed a new polygon wall boundary model for fully
explicit algorithms (Explicit-MPS [7]: E-MPS), called the Explicitly Represented
Polygon (ERP) wall boundary model [8] to compose more accurate MPS-FE
method. The ERP model is formulated such that it satisfies the pressure Neumann
boundary condition and the slip/no-slip boundary condition, without requiring the
generation of virtual particles or treating angled edges as exceptional cases.
Moreover, the ERP model eliminates the problem of force imbalance on the
boundaries, which occurs in conventional models.
2 ERP Wall Boundary Model for Explicit-MPS Method
Regarding the wall boundary treatments, research has made greater progress for the
SPH method [9], which is one of mesh-free particle methods. The repulsive-force
model [10] has been developed in order to avoid penetration of fluid particles across
wall boundaries. Although this model is relatively easy to implement, it causes the
instability of fluid particles near wall boundaries because the boundary conditions
are not satisfied. On the other hand, the ghost (mirror) particle approach [11] is
widely used to satisfy the boundary conditions on walls. In this approach, virtual
particle is generated at reflectional position across the wall of each fluid particle.
These mirror particles are given pressure and velocity values so that the pressure
Neumann boundary condition and slip/no-slip condition are satisfied. However, this
304
N. Mitsume et al.