64
T. T. Bui and S. Nakata
is distributed sequential as described in [6]: inflow particles, fluid particles, outflow
particles and boundary particles at every time step. For the simulation with the above
inflow/outflow algorithm, a re-arranged process for the structure of total particles is
required at every time step which leads to high computational cost.
The advantage of our approach is to preserve the total number of particles throughout
the simulation by inserting inflow particles immediately into the computational domain
after passing the outlet zone. In addition, the management of total particles are based
only on the type of particles. Hence, this avoids the re-arranged process for the structure
of total particles at every time step.
Due to the hybrid of in/out-flow boundaries and periodic boundary condition, this
approach is flexible to solve various kinds of test cases whether prescribed boundary
condition or non-prescribed boundary condition.
+ Boundaries with Prescribed Values
Let us assume that velocity and pressure conditions at the inlet are prescribed. The
velocity and pressure are enforced the desired values. The inflow particles that cross the
inflow zone become fluid particles and they will be treated as fluid particles. The fluid
particles pass through fluid zone become outflow particles and they will be treated as
outflow particles. The outflow particles are either possible to impose specific outflow
conditions as inflow particles or handling as fluid particles. Outflow particles that pass
through outflow zone will be re-inserted at inlet zone with same y-coordinate positions
and the values are same the desired values at the inflow zone.
+ Boundaries with Non-prescribed Values
Let us assume that velocity and pressure conditions at the inlet are non-prescribed. The
in/out-flow particles will be treated as fluid particles that evolve following the SPH
governing equations. On the contrary, the values of new inflow particles are calculated
as Eq. (7) and Eq. (8).
ρ
inlet
i
=
N
j∈fluid ρ j
m j
ρ j
W ij
N
j∈fluid
m j
ρ j
W ij
(7)
u
inlet
i
=
N
j∈fluid u j
m j
ρ j
W ij
N
j∈fluid
m j
ρ j
W ij
(8)
4 Test Cases
Two test cases of viscous open-channel flow in the laminar regime were simulated with
prescribed value and non-prescribed value. The results obtained through simulation by
I. Federico [6] have been used here as a reference solution.
In this simulation, fluid flow moves with a distribution of velocity u(z) for 2D channel
flow as equation:
u(z) =
ρgs 0
2μ
2hz − z
2
(9)
T. T. Bui and S. Nakata
is distributed sequential as described in [6]: inflow particles, fluid particles, outflow
particles and boundary particles at every time step. For the simulation with the above
inflow/outflow algorithm, a re-arranged process for the structure of total particles is
required at every time step which leads to high computational cost.
The advantage of our approach is to preserve the total number of particles throughout
the simulation by inserting inflow particles immediately into the computational domain
after passing the outlet zone. In addition, the management of total particles are based
only on the type of particles. Hence, this avoids the re-arranged process for the structure
of total particles at every time step.
Due to the hybrid of in/out-flow boundaries and periodic boundary condition, this
approach is flexible to solve various kinds of test cases whether prescribed boundary
condition or non-prescribed boundary condition.
+ Boundaries with Prescribed Values
Let us assume that velocity and pressure conditions at the inlet are prescribed. The
velocity and pressure are enforced the desired values. The inflow particles that cross the
inflow zone become fluid particles and they will be treated as fluid particles. The fluid
particles pass through fluid zone become outflow particles and they will be treated as
outflow particles. The outflow particles are either possible to impose specific outflow
conditions as inflow particles or handling as fluid particles. Outflow particles that pass
through outflow zone will be re-inserted at inlet zone with same y-coordinate positions
and the values are same the desired values at the inflow zone.
+ Boundaries with Non-prescribed Values
Let us assume that velocity and pressure conditions at the inlet are non-prescribed. The
in/out-flow particles will be treated as fluid particles that evolve following the SPH
governing equations. On the contrary, the values of new inflow particles are calculated
as Eq. (7) and Eq. (8).
ρ
inlet
i
=
N
j∈fluid ρ j
m j
ρ j
W ij
N
j∈fluid
m j
ρ j
W ij
(7)
u
inlet
i
=
N
j∈fluid u j
m j
ρ j
W ij
N
j∈fluid
m j
ρ j
W ij
(8)
4 Test Cases
Two test cases of viscous open-channel flow in the laminar regime were simulated with
prescribed value and non-prescribed value. The results obtained through simulation by
I. Federico [6] have been used here as a reference solution.
In this simulation, fluid flow moves with a distribution of velocity u(z) for 2D channel
flow as equation:
u(z) =
ρgs 0
2μ
2hz − z
2
(9)