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)[source]#

Bases: CoefficientMatrix, BaseScatteringDoinikov1994

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

Parameters:

  • f (Frequency | float | int) – Frequency [Hz]

  • R_0 (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 (None | 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]
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 (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 (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)[source]#

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

Parameters:

n (int) – order

Return type:

complex

alpha_n(n)[source]#

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

Parameters:

n (int) – order

Return type:

complex

beta_hat_n(n)[source]#

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

Parameters:

n (int) – order

Return type:

complex

beta_n(n)[source]#

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 (None | 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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

  • scattered (bool) – add scattered field

  • incident (bool) – add incident

  • mode (None | 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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

  • scattered (bool) – scattered field contribution

  • incident (bool) – incident field contribution

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

    Default: None

Return type:

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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

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

    Default: None

Return type:

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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

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

    Default: None

Return type:

complex | NDArray

radial_particle_velocity(r, theta, t, mode=None)[source]#

Particle velocity in radial direction

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

Parameters:

  • r (float | NDArray | list[float]) – radial coordinate [m]

  • theta (float | NDArray | list[float]) – tangential coordinate [rad]

  • t (float | NDArray | list[float]) – time [s]

  • mode (None | 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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

  • scattered (bool) – scattered field contribution

  • incident (bool) – incident field contribution

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

    Default: None

Return type:

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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

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

Return type:

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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

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

    Default: None

Return type:

complex | NDArray

tangential_particle_velocity(r, theta, t, mode=None)[source]#

Particle velocity in tangential direction

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

Parameters:

  • r (float | NDArray | list[float]) – radial coordinate [m]

  • theta (float | NDArray | list[float]) – tangential coordinate [rad]

  • t (float | NDArray | list[float]) – time [s]

  • mode (None | 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 (float | Sequence) – radial coordinate [m]

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

  • t (float | Sequence) – time [s]

  • scattered (bool) – add scattered field

  • incident (bool) – add incident

  • mode (None | 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