vortex_creation module

class IMTreatment.vortex_creation.vortex_creation.BurgerVortex(x0=0.0, y0=0.0, alpha=1e-06, ksi=1.0, viscosity=1e-06, movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a Burger Vortex, a stationnary self-similar flow, caused by the balance between vorticity creation at the center and vorticity diffusion.

Notes

Analytical Vortex Solutions to the Navier-Stokes Equation. Thesis for the degree of Doctor of Philosophy, Växjö University, Sweden 2007.

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.CustomField(funct, unit_values='', idi=0)

Bases: object

Representing a custom field.

Parameters:funct (function) – Representing the field. Has to take (x, y) as input and return (Vx, Vy).

copy()

get_vector(x, y)

get_vector_field(axe_x, axe_y, unit_x='', unit_y='')

class IMTreatment.vortex_creation.vortex_creation.FreeVortex(x0=0.0, y0=0.0, gamma=1.0, movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a Free (irrotational) Vortex. Due to its definition, the center of the vortex is a singular point (V = inf) set to 0 in this implementation.

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.HillVortex(x0=0, y0=0, U=1.0, rv=1.0, rot_dir=1, unit_values='', movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a Hill Vortex, a convected vortex sphere in a inviscid flow.

Notes

Analytical Vortex Solutions to the Navier-Stokes Equation. Thesis for the degree of Doctor of Philosophy, Växjö University, Sweden 2007.

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.HsvSystem(u_D, D, h, delta, vertical_wall=True)

Bases: IMTreatment.vortex_creation.vortex_creation.VortexSystem

class IMTreatment.vortex_creation.vortex_creation.LambChaplyginVortex(x0=0, y0=0, U=1.0, rv=1.0, Bessel_root_nmb=1, movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a Lamb-Chaplygin dipole vortex, with potential flow in the exterior region, and a linear relation between stream function and vorticity in the inner region.

Notes

Analytical Vortex Solutions to the Navier-Stokes Equation. Thesis for the degree of Doctor of Philosophy, Växjö University, Sweden 2007.

J(order, x)

Return the value of the Bessel function with the given order ar the given point.

Parameters:

• order (number) – Order of the Bessel function
• x (number) – Value where we want the Bessel function evaluation.

Returns:

y – Bessel function value at ‘x’

Return type:

number

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.LambOseenVortex(x0=0, y0=0, ksi=1.0, t=1.0, viscosity=1e-06, movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a Lamb-Oseen Vortex, a vortex with decay due to viscosity. (satisfy NS)

Notes

Analytical Vortex Solutions to the Navier-Stokes Equation. Thesis for the degree of Doctor of Philosophy, Växjö University, Sweden 2007.

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.PersoVortex(x0=0, y0=0, radius=1.0, vort_max=None, circ=None, node_ratio=0.0, nu=1e-06, movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a slice of a 3D vortex.

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.RankineVortex(x0=0.0, y0=0.0, circ=1.0, rv=1.0, movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a Rankine Vortex, with an inner zone or forced vortex, and an outer zone of free vortex.

Notes

Giaiotti, DARIO B., et FULVIO Stel. « The Rankine vortex model ». PhD course on Environmental Fluid Mechanics-ICTP/University of Trieste, 2006.

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.SolidVortex(x0=0.0, y0=0.0, omega=1.0, movable=True, idi=0)

Bases: IMTreatment.vortex_creation.vortex_creation.Vortex

Representing a solid rotation.

get_vector(x, y)

Return the velocity vector at the given point.

class IMTreatment.vortex_creation.vortex_creation.StepSystem(u_D, H, h, delta)

Bases: IMTreatment.vortex_creation.vortex_creation.VortexSystem

class IMTreatment.vortex_creation.vortex_creation.Vortex(x0, y0, movable, idi=0)

Bases: object

copy()

get_vector_field(axe_x, axe_y, unit_x='', unit_y='')

symetrize()

Return a symetrized copy of the vortex

x0

y0

class IMTreatment.vortex_creation.vortex_creation.VortexSystem

Bases: object

Representing a set of vortex.

add_custom_field(custfield)

Add a custom field to the vortex system

Parameters:custfield (CustomField object) – Custom field to add.

add_vortex(vortex)

Add a vortex, or a custom field to the set.

Parameters:vortex (Vortex or CustomField object) – vortex or field to add to the set

add_wall(wall)

Add a wall to the vortex system

Parameters:wall (Wall object) – Wall to add.

copy()

Return a copy.

display()

Display a representation of the vortex system

display_compounded_vector(x, y, scale=1.0, detailed=False)

Display the compounded vector in ‘x’, ‘y’ position.

get_compounded_vector(x, y, detailed=False)

Return a list f vector, for each structure of the system

Parameters:

• y (x,) – Wanted vector coordinates
• detailed (boolean, optional) – If ‘False’ (default), vortex contribution and its imaginary vortex contribution are summed up. Else, return one vector for each contribution.

Returns:

• vects (Nx2 array of numbers) – Vectors associated to vortex contribution
• vortex_ids (Nx1 array of integer) – Associated id
• verts_cf (Mx2 array of numbers) – Vectors associated to custom fields contribution
• cf_ids (Mx1 array of integer) – Associated id

get_evolution(dt=1.0)

Change the position of the vortex, according to the resulting velocity field and the time step.

Parameters:dt (number) – time step. Returns:vs – New vortex system at t+dt Return type:VortexSystem object

get_temporal_vector_field(dt, axe_x, axe_y, nmb_it, unit_x='', unit_y='', unit_time='')

get_vector(x, y, vortex_ids='all', cf_ids='all')

Return the resulting velocity vector, at the given point.

Parameters:

• y (x,) – Position of the wanted vector.
• vortex_ids (list of integers, 'all' or 'none') – Can be used to filter the wanted vortex influence by ids.
• cf_ids (list of integers, 'all' or 'none') – Can be used to filter the wanted custom fields influence by ids.

Returns:

Vx, Vy – Velocity components.

Return type:

numbers

get_vector_field(axe_x, axe_y, unit_x='', unit_y='')

Return a vector field on the given grid

Parameters:

• axe_y (axe_x,) – x and y axis
• unit_y (unit_x,) – Axis unities

Returns:

vf – .

Return type:

VectorField object

get_velocity_map(axe_x, axe_y, vort, unit_x='m', unit_y='m')

Return the velocity map of vortex ‘vort’ on the vortex system (velocity that the vortex ‘vort’ will have if placed at different space position on the vortex system)

get_vortex_evolution(dt, nmb_it, unit_time='')

refresh_imaginary_vortex()

remove_vortex(ind)

Remove a vortex or a custom field from the set.

Parameters:ind (integer) – Vortex indice to remove.

class IMTreatment.vortex_creation.vortex_creation.Wall(x=None, y=None)

Bases: object

Representing a wall

get_symmetry(pt)

Give the symmetry of ‘pt’ according to the wall.