ScatteringField

Examples using this class are:

class osaft.solutions.doinikov1994compressible.scattering.ScatteringField(f, R_0, rho_s, c_s, eta_s, zeta_s, rho_f, c_f, eta_f, zeta_f, p_0, wave_type, position, N_max=5)

Bases: CoefficientMatrix, BaseScatteringDoinikov1994

Scattering field of Doinikov (viscous fluid-viscous sphere; 1994)

Parameters:

• f (Union[Frequency, float, int]) – Frequency [Hz]

• R_0 (Union[Sphere, float, int]) – Radius of the sphere [m]

• rho_s (float) – Density of the sphere [kg/m^3]

• c_s (float) – Speed of sound of in the sphere [m/s]

• eta_s (float) – shear viscosity of in the sphere [Pa s]

• zeta_s (float) – bulk viscosity of in the sphere [Pa s]

• rho_f (float) – Density of the fluid [kg/m^3]

• c_f (float) – Speed of sound of the fluid [m/s]

• eta_f (float) – shear viscosity [Pa s]

• zeta_f (float) – bulk viscosity [Pa s]

• p_0 (float) – Pressure amplitude of the field [Pa]

• position (float) – Position within the standing wave field [m]

• wave_type (WaveType) – Type of wave, traveling or standing

• N_max (Optional[int], optional) – Highest order mode included in the computation [-]

  Default: 5

Public Data Attributes:

Inherited from CoefficientMatrix

x_hat	Product of k_s and R_0 \(\hat{x}=k_s R_0\)
x_hat_v	Product of k_vs and R_0 \(\hat{x}_v=\hat{k}_s R_0\)

Inherited from BaseDoinikov1994Compressible

supported_wavetypes
rho_s	Wraps to osaft.core.solids.RigidSolid.rho_s
kappa_s	Wraps to osaft.core.fluids.ViscousFluid.kappa_f
k_s	Wraps to osaft.core.fluids.ViscousFluid.k_f
k_vs	Wraps to osaft.core.fluids.ViscousFluid.k_v
c_s	Wraps to osaft.core.fluids.ViscousFluid.c_f
eta_s	Wraps to osaft.core.fluids.ViscousFluid.eta_f
zeta_s	Wraps to osaft.core.fluids.ViscousFluid.zeta_f

Inherited from BaseDoinikov1994

x	Product of k_f and R_0 \(\hat{x}=k_f R_0\)
x_v	Product of k_v and R_0 \(x_v=k_v R_0\)
x_0	Real part of \(x\)
norm_delta	normalized viscous boundary thickness \(\tilde{\delta}=\frac{\delta}{R_0}\)
position	Wraps to osaft.core.backgroundfields.BackgroundField.position
p_0	Wraps to osaft.core.backgroundfields.BackgroundField.p_0
wave_type	Wraps to osaft.core.backgroundfields.BackgroundField.wave_type
rho_f	Wraps to osaft.core.fluids.ViscousFluid.rho_f
c_f	Wraps to osaft.core.fluids.ViscousFluid.c_f
eta_f	Wraps to osaft.core.fluids.ViscousFluid.eta_f
zeta_f	Wraps to osaft.core.fluids.ViscousFluid.zeta_f
rho_t	Returns the ratio of the densities \(\tilde{\rho}=\frac{\rho_f}{\rho_s}\)
kappa_f	Wraps to osaft.core.fluids.ViscousFluid.kappa_f
k_f	Wraps to osaft.core.fluids.ViscousFluid.k_f
k_v	Wraps to osaft.core.fluids.ViscousFluid.k_v
delta	Wraps to osaft.core.fluids.ViscousFluid.delta
abs_pos	Wraps to osaft.core.backgroundfields.BackgroundField.abs_pos

Inherited from BaseSphereFrequencyComposite

R_0	Wrapper for osaft.core.geometries.Sphere.R_0
area	Wrapper for osaft.core.geometries.Sphere.area
volume	Wrapper for osaft.core.geometries.Sphere.volume

Inherited from BaseFrequencyComposite

f	wrapper for osaft.core.frequency.Frequency.f
omega	wrapper for osaft.core.frequency.Frequency.omega

Inherited from BaseSolution

supported_wavetypes
wave_type	returns the wave type of the solution

Inherited from BaseScatteringDoinikov1994

k_f	Returns the wave number in the fluid \(k_f\) [1/m]
k_v	Returns the viscous wave number in the fluid \(k_v\) [1/m]
field
omega
R_0
rho_f

Inherited from BaseScattering

N_max	Cutoff mode number for infinite sums
field
omega
R_0
rho_f
k_f

Public Methods:

alpha_n(n)	coefficient \(\alpha_n\) (3.13) and (3.20)
beta_n(n)	coefficient \(\beta_n\) (3.13) and (3.20)
alpha_hat_n(n)	coefficient \(\alpha_hat_n\) (3.13) and (3.20)
beta_hat_n(n)	coefficient \(\beta_hat_n\) (3.13) and (3.20)
radial_particle_velocity(r, theta, t[, mode])	Particle velocity in radial direction
tangential_particle_velocity(r, theta, t[, mode])	Particle velocity in tangential direction

Inherited from CoefficientMatrix

det_M_n(n[, column])	Determinant of the matrix M for the mode n
M(n)	Matrix M of order n
N(n)	Vector N

Inherited from BaseDoinikov1994

A_in(n)

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Inherited from BaseFrequencyComposite

input_variables()

Returns all properties that are settable.

Inherited from BaseSolution

copy()	Returns a copy of the object
check_wave_type()	Checks if wave_type is in supported_wavetypes

Inherited from BaseScatteringDoinikov1994

potential_coefficient(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
V_r_sc(n, r)	Radial scattering field velocity term of mode n without Legendre coefficients
V_theta_sc(n, r)	Tangential scattering field velocity term of mode n without Legendre coefficients
A_in(n)	Incoming wave amplitude
alpha_n(n)	\(\alpha_n\) coefficient
beta_n(n)	\(\beta_n\) coefficient

Inherited from BaseScattering

radial_acoustic_fluid_velocity(r, theta, t, ...)	Returns the value for the radial acoustic velocity in [m/s].
tangential_acoustic_fluid_velocity(r, theta, ...)	Returns the value for the tangential acoustic velocity in [m/s].
pressure(r, theta, t, scattered, incident[, ...])	Returns the acoustic pressure [Pa].
potential_coefficient(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
velocity_potential(r, theta, t, scattered, ...)	Returns the velocity potential of the fluid in [m^2/s].
radial_particle_velocity(r, theta, t[, mode])	Returns the value for the radial particle velocity in [m/s].
tangential_particle_velocity(r, theta, t[, mode])	Returns the value for the tangential particle velocity in [m/s].
radial_particle_displacement(r, theta, t[, mode])	Particle displacement in radial direction
tangential_particle_displacement(r, theta, t)	Particle displacement in tangential direction
radial_mode_superposition(radial_func, r, ...)	Returns either a single mode (mode=int) or a the sum until N_max (mode=None).
tangential_mode_superposition(...)	Returns either a single mode (mode=int) or a the sum until N_max (mode=None).
V_r_i(n, r)	Radial incident field velocity term of mode n without Legendre coefficients
V_theta_i(n, r)	Tangential incident field velocity term of mode n without Legendre coefficients
V_r_sc(n, r)	Radial scattering field velocity term of mode n without Legendre coefficients
V_theta_sc(n, r)	Tangential scattering field velocity term of mode n without Legendre coefficients
V_r(n, r, scattered, incident)	Superposition of V_r_sc() and V_r_i() depending on scattered and incident
V_theta(n, r, scattered, incident)	Superposition of V_theta_sc() and V_theta_i() depending on scattered and incident

---

A_in(n)

Wraps to osaft.core.backgroundfields.BackgroundField.A_in

Parameters:

n (int) – mode number

Return type:

complex

M(n)

Matrix M of order n

Parameters:

n (int) – order

Return type:

ndarray

N(n)

Vector N

Parameters:

n (int) –

Return type:

ndarray

V_r(n, r, scattered, incident)

Superposition of V_r_sc() and V_r_i() depending on scattered and incident

At least one of the two must be True.

Parameters:

• n (int) – mode

• r (float) – radial coordinate [m]

• scattered (bool) – add scattered field

• incident (bool) – add incident

Return type:

complex

V_r_i(n, r)

Radial incident field velocity term of mode n without Legendre coefficients

Returns radial incident field velocity in [m/s]

Parameters:

• n (int) – mode

• r (Union[float, Sequence]) – radial coordinate [m]

Return type:

complex

V_r_sc(n, r)

Radial scattering field velocity term of mode n without Legendre coefficients

Returns radial scattering field velocity in [m/s]

Parameters:

• n (int) – mode

• r (float) – radial coordinate [m]

Return type:

complex

V_theta(n, r, scattered, incident)

Superposition of V_theta_sc() and V_theta_i() depending on scattered and incident

At least one of the two must be True.

Parameters:

• n (int) – mode

• r (float) – radial coordinate [m]

• scattered (bool) – add scattered field

• incident (bool) – add incident

Return type:

complex

V_theta_i(n, r)

Tangential incident field velocity term of mode n without Legendre coefficients

Returns tangential incident field velocity in [m/s]

Parameters:

• n (int) – mode

• r (Union[float, Sequence]) – radial coordinate [m]

Return type:

complex

V_theta_sc(n, r)

Tangential scattering field velocity term of mode n without Legendre coefficients

Returns tangential scattering field velocity in [m/s]

Parameters:

• n (int) – mode

• r (float) – radial coordinate [m]

Return type:

complex

alpha_hat_n(n)

coefficient \(\alpha_hat_n\) (3.13) and (3.20)

Parameters:

n (int) – order

Return type:

complex

alpha_n(n)

coefficient \(\alpha_n\) (3.13) and (3.20)

Parameters:

n (int) – order

Return type:

complex

beta_hat_n(n)

coefficient \(\beta_hat_n\) (3.13) and (3.20)

Parameters:

n (int) – order

Return type:

complex

beta_n(n)

coefficient \(\beta_n\) (3.13) and (3.20)

Parameters:

n (int) – order

Return type:

complex

check_wave_type()

Checks if wave_type is in supported_wavetypes

Raises:

WrongWaveTypeError – If wave_type is not supported

Return type:

None

copy()

Returns a copy of the object

Return type:

BaseSolution

det_M_n(n, column=None)

Determinant of the matrix M for the mode n

Parameters:

• n (int) – mode

• column (Optional[int], optional) – the l`th coefficient is replaced with the vector `N

  Default: None

Return type:

complex

classmethod input_variables()

Returns all properties that are settable.

Returns a list of the names of all properties that are settable, i.e. all properties that wrap a PassiveVariable.

Return type:

list[str]

potential_coefficient(n)

Wrapper to the fluid scattering coefficients for an inviscid fluid

This method must be implemented by every theory to have a common interface for other modules.

Parameters:

n (int) – mode

Return type:

complex

pressure(r, theta, t, scattered, incident, mode=None)

Returns the acoustic pressure [Pa].

Parameters:

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• scattered (bool) – add scattered field

• incident (bool) – add incident

• mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

  Default: None

Return type:

complex

radial_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)

Returns the value for the radial acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters:

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• scattered (bool) – scattered field contribution

• incident (bool) – incident field contribution

• mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

  Default: None

Return type:

Union[complex, ndarray]

radial_mode_superposition(radial_func, r, theta, t, mode=None)

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_{\text{mode}}(r) \,P_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t} \sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P_n(\cos\theta)\]

where \(f_\text{n}(r)\) is the radial_func(n, r) passed to the method.

Parameters:

• radial_func (Callable[[int, float], complex]) – radial function dependent on r

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

  Default: None

Return type:

Union[complex, ndarray]

radial_particle_displacement(r, theta, t, mode=None)

Particle displacement in radial direction

Returns the value of the particle displacement in radial direction in [m]

Parameters:

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• mode (Optional[int], optional) – specific mode number of interest; if None that all modes until N_max

  Default: None

Return type:

Union[complex, ndarray]

radial_particle_velocity(r, theta, t, mode=None)

Particle velocity in radial direction

Returns the value of the particle velocity in radial direction in [m/s]

Parameters:

• r (Union[float, ndarray, list[float]]) – radial coordinate [m]

• theta (Union[float, ndarray, list[float]]) – tangential coordinate [rad]

• t (Union[float, ndarray, list[float]]) – time [s]

• mode (Optional[int], optional) – mode to be plotted, if None then sum of all mode up to N_max

  Default: None

Return type:

complex

tangential_acoustic_fluid_velocity(r, theta, t, scattered, incident, mode=None)

Returns the value for the tangential acoustic velocity in [m/s].

This method must be implemented by every theory to have a common interface for other modules.

Parameters:

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• scattered (bool) – scattered field contribution

• incident (bool) – incident field contribution

• mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

  Default: None

Return type:

Union[complex, ndarray]

tangential_mode_superposition(tangential_func, r, theta, t, mode)

Returns either a single mode (mode=int) or a the sum until N_max (mode=None).

If mode=int the formula is

\[e^{-i\omega t}\, f_\text{mode}(r) \,P^1_{\text{mode}}(\cos\theta)\]

If mode=None the formula is

\[e^{-i\omega t}\sum_{n=0}^{\text{N}_{\text{max}}} \,f_n(r) \,P^1_n(\cos\theta)\]

where \(f_n(r)\) is the tangential_func(n, r) passed to the method.

Parameters:

• tangential_func (Callable[[int, float], complex]) – tangential function dependent on r

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• mode (int) – specific mode number of interest; if None then all modes until N_max

Return type:

Union[complex, ndarray]

tangential_particle_displacement(r, theta, t, mode=None)

Particle displacement in tangential direction

Returns the value of the particle displacement in tangential direction in [m]

Parameters:

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• mode (Optional[int], optional) – specific mode number of interest; if None that all modes until N_max

  Default: None

Return type:

Union[complex, ndarray]

tangential_particle_velocity(r, theta, t, mode=None)

Particle velocity in tangential direction

Returns the value of the particle velocity in tangential direction in [m/s]

Parameters:

• r (Union[float, ndarray, list[float]]) – radial coordinate [m]

• theta (Union[float, ndarray, list[float]]) – tangential coordinate [rad]

• t (Union[float, ndarray, list[float]]) – time [s]

• mode (Optional[int], optional) – mode to be plotted, if None then sum of all mode up to N_max

  Default: None

Return type:

complex

velocity_potential(r, theta, t, scattered, incident, mode=None)

Returns the velocity potential of the fluid in [m^2/s].

Parameters:

• r (Union[float, Sequence]) – radial coordinate [m]

• theta (Union[float, Sequence]) – tangential coordinate [rad]

• t (Union[float, Sequence]) – time [s]

• scattered (bool) – add scattered field

• incident (bool) – add incident

• mode (Optional[int], optional) – specific mode number of interest; if None then all modes until N_max

  Default: None

Return type:

complex

property N_max

Cutoff mode number for infinite sums

Getter:

returns number of infinite sum term

Setter:

automatically invokes osaft.core.variable.BaseVariable.notify()

property R_0: float

Wrapper for osaft.core.geometries.Sphere.R_0

property abs_pos: float

Wraps to osaft.core.backgroundfields.BackgroundField.abs_pos

property area: float

Wrapper for osaft.core.geometries.Sphere.area

property c_f: float

Wraps to osaft.core.fluids.ViscousFluid.c_f

property c_s: float

Wraps to osaft.core.fluids.ViscousFluid.c_f

property delta: float

Wraps to osaft.core.fluids.ViscousFluid.delta

property eta_f: float

Wraps to osaft.core.fluids.ViscousFluid.eta_f

property eta_s: float

Wraps to osaft.core.fluids.ViscousFluid.eta_f

property f: float

wrapper for osaft.core.frequency.Frequency.f

property k_f: complex

Wraps to osaft.core.fluids.ViscousFluid.k_f

property k_s: complex

Wraps to osaft.core.fluids.ViscousFluid.k_f

property k_v: complex

Wraps to osaft.core.fluids.ViscousFluid.k_v

property k_vs: complex

Wraps to osaft.core.fluids.ViscousFluid.k_v

property kappa_f: float

Wraps to osaft.core.fluids.ViscousFluid.kappa_f

property kappa_s: float

Wraps to osaft.core.fluids.ViscousFluid.kappa_f

property norm_delta: float

normalized viscous boundary thickness \(\tilde{\delta}=\frac{\delta}{R_0}\)

property omega: float

wrapper for osaft.core.frequency.Frequency.omega

property p_0: float

Wraps to osaft.core.backgroundfields.BackgroundField.p_0

property position: float

Wraps to osaft.core.backgroundfields.BackgroundField.position

property rho_f: float

Wraps to osaft.core.fluids.ViscousFluid.rho_f

property rho_s: float

Wraps to osaft.core.solids.RigidSolid.rho_s

property rho_t: float

Returns the ratio of the densities \(\tilde{\rho}=\frac{\rho_f}{\rho_s}\)

property volume: float

Wrapper for osaft.core.geometries.Sphere.volume

property wave_type: WaveType

Wraps to osaft.core.backgroundfields.BackgroundField.wave_type

property x: complex

Product of k_f and R_0 \(\hat{x}=k_f R_0\)

property x_0: complex

Real part of \(x\)

property x_hat: complex

Product of k_s and R_0 \(\hat{x}=k_s R_0\)

property x_hat_v: complex

Product of k_vs and R_0 \(\hat{x}_v=\hat{k}_s R_0\)

property x_v: complex

Product of k_v and R_0 \(x_v=k_v R_0\)

property zeta_f: float

Wraps to osaft.core.fluids.ViscousFluid.zeta_f

property zeta_s: float

Wraps to osaft.core.fluids.ViscousFluid.zeta_f