Exemple X : 3D Moving sharp immersed Boundary

In this example, we study the flow around a moving sphere of unit diameter at constant speed for a Reynold number of Re=50. This is done using the Sharp interface immersed boundary method. This example can be solve using the gls_sharp_navier_stokes_3d solver.

NOTE : This simulation only follows the first few moments of the displacement of the particle (0.25 seconde). The flow won't have the time to establish itself in this case. If let the flow establish itself, a longer channel must be given as the domain and a much longer simulation time must be used.

The following schematic describes the simulation.

INSERT IMAGE

We consider slip boundary condition on all the boundaries parallels to the trajectory of the particle and open boundary at each of the boundary perpendicular to the trajectory of the particle.

# --------------------------------------------------
# Boundary Conditions
#---------------------------------------------------
subsection boundary conditions
set number                  = 4

    subsection bc 1
	set id = 2
        set type              = slip
    end
    subsection bc 2
	set id = 3
        set type              = slip
    end
    subsection bc 3
	set id = 4
        set type              = slip
    end
    subsection bc 4
	set id = 5
        set type              = slip
    end

end

The definition of the mesh is done directly through deal.ii tools for mesh generation:

#---------------------------------------------------
# Mesh
#---------------------------------------------------
subsection mesh
    set type                 = dealii
    set grid type            = subdivided_hyper_rectangle
    set grid arguments       = 2,1,1: 0,0,0 : 32,16,16 : true
    set initial refinement   = 5
end

We fix the velocity of the particle to one and varies the Reynolds number by varying the kinematic viscosity of the flow.

#---------------------------------------------------
# Physical Properties
#---------------------------------------------------
subsection physical properties
    set kinematic viscosity            = 0.02
end

The motion of the particle require the use of a transient solver. At the moment only BDF schemes are compatible with moving sharp interface. In this case we use BDF1. In this example we only simulate the first 0.25 seconde. To do so we use a time step of 0.025 seconde.

# --------------------------------------------------
# Simulation and IO Control
#---------------------------------------------------
subsection simulation control
  set method                  = bdf1
  set time step               = 0.025 # Time step
  set time end                = 0.25     # End time of simulation
  set output name             = moving_sphere # Prefix for VTU outputs
  set output frequency        = 1       # Frequency of simulation output
  set subdivision             = 1       # Mesh subdivision when outpu
end

At this point we have defined almost all the elements necessary to this example except the moving sphere. This is done in the IB particles section (See Exemple 10 for more detail on the general parameters of this section). The particle is defined in the same way in 3d as in 2d. To put the particle in motion one only need to specify the particle velocity to be something other than zero. We also add the fact that the boolean variable integrate motion is kept false as this is only need to be true when particle trajectories are subject to the hydrodynamic forces applied to the particle.