Nonreflecting Outlet Boundary Conditions for Smoothed Particle Hydrodynamics
65
where ρ is density, g is the gravity acceleration, s 0 is the bottom slope, h is the surface
depth, μ is the dynamic viscosity and z is the vertical abscissa which origin is located
at the channel bottom
The Reynolds number is calculated by equation:
Re =
ρUh
μ
(10)
where velocity U is evaluated be the average velocity profile
U =
1
h
h
∫
0
u(z)dz
(11)
The length of fluid domain is L = 2 h and the slope s 0 = 0.001. For both cases, the fluid
particles are initialized with analytical solution by Eq. (9). The sound speed is selected
equal 10u (z = h). The model of simulation depicts as Fig. 3.
Fig. 3. Sketch of the elementary fluid domain.
The tensile instability in SPH is always challenging, especially for the simulation
with high Reynolds numbers. In this simulation, we use a particle shifting technique in
[12] to remove for this issue of simulation.
4.1 Viscous Open-Channel Flow with Prescribed Boundary Condition
In this case, the initial boundary condition is imposed as follows:
z f (t = 0) = z i (t) = h
u f (z, t = 0) = u i (z, t) =
ρgs 0
2μ
2hz − z
2
p f (z, t = 0) = p i (z, t) = ρg(z − h)
(12)
Velocity and pressure at the inflow zone are enforced desired values throughout
simulation. On the contrary, at the outflow zone, the outflow particles are treated as
fluid particles where initial information the same as the inflow particles and then their
information evolves in accordance with the SPH governing equations.
65
where ρ is density, g is the gravity acceleration, s 0 is the bottom slope, h is the surface
depth, μ is the dynamic viscosity and z is the vertical abscissa which origin is located
at the channel bottom
The Reynolds number is calculated by equation:
Re =
ρUh
μ
(10)
where velocity U is evaluated be the average velocity profile
U =
1
h
h
∫
0
u(z)dz
(11)
The length of fluid domain is L = 2 h and the slope s 0 = 0.001. For both cases, the fluid
particles are initialized with analytical solution by Eq. (9). The sound speed is selected
equal 10u (z = h). The model of simulation depicts as Fig. 3.
Fig. 3. Sketch of the elementary fluid domain.
The tensile instability in SPH is always challenging, especially for the simulation
with high Reynolds numbers. In this simulation, we use a particle shifting technique in
[12] to remove for this issue of simulation.
4.1 Viscous Open-Channel Flow with Prescribed Boundary Condition
In this case, the initial boundary condition is imposed as follows:
z f (t = 0) = z i (t) = h
u f (z, t = 0) = u i (z, t) =
ρgs 0
2μ
2hz − z
2
p f (z, t = 0) = p i (z, t) = ρg(z − h)
(12)
Velocity and pressure at the inflow zone are enforced desired values throughout
simulation. On the contrary, at the outflow zone, the outflow particles are treated as
fluid particles where initial information the same as the inflow particles and then their
information evolves in accordance with the SPH governing equations.