BaseScatteringDoinikov2021

Examples using this class are:

Doinikov 2021 Viscous - Convergence Study

Fluid: Acoustic velocity plots with arrows

class osaft.solutions.basedoinikov2021.scattering.BaseScatteringDoinikov2021(f, R_0, rho_s, E_s, nu_s, fluid, p_0, wave_type, position=None, N_max=5)[source]

Bases: CoefficientMatrix, BaseScattering, ABC

Scattering field class for Doinikov (viscous fluid-elastic sphere; 2021)

Parameters

f (Frequency | float) – frequency [Hz]
R_0 (Sphere | float) – radius [m]
rho_s (float) – density of the particle [kg/m^3]
E_s (float) – Young’s modulus of the particle [Pa]
nu_s (float) – Poisson’s ratio of the particle [-]
fluid (ViscousFluid | ViscoelasticFluid) – Fluid instance of the model
p_0 (float) – pressure amplitude [Pa]
wave_type (WaveType) – wave type
position (None | float, optional) – position in the standing wave field [m]
Default: None
N_max (int, optional) –
Default: 5

Public Data Attributes:

`range_N_max`	Returns `range(0, N_max + 1)`
`range_1_N_max`	Returns `range(1, N_max + 1)`
`range_2_N_max`	Returns `range(2, N_max + 1)`

Inherited from BaseDoinikov

`supported_wavetypes`
`eta`	Fluid shear viscosity.
`zeta`	Fluid bulk viscosity.
`x_l`	Dimensionless primary wavenumber in the solid
`x_t`	Dimensionless secondary wavenumber in the solid
`x_f`	Dimensionless acoustic wavenumber in the fluid
`x_v`	Dimensionless viscous wavenumber in the fluid
`rho_s`	Wraps to `osaft.core.solids.ElasticSolid.rho_s`
`E_s`	Wraps to `osaft.core.solids.ElasticSolid.E_s`
`nu_s`	Wraps to `osaft.core.solids.ElasticSolid.nu_s`
`k_l`	Wraps to `osaft.core.solids.ElasticSolid.k_l`
`k_t`	Wraps to `osaft.core.solids.ElasticSolid.k_t`
`rho_f`	Wraps to `osaft.core.fluids.ViscousFluid.rho_0` or to `osaft.core.fluids.ViscoelasticFluid.rho_0`
`c_f`	Wraps to `osaft.core.fluids.ViscousFluid.c_f` or to `osaft.core.fluids.ViscoelasticFluid.c_f`
`eta_f`	Wraps to `osaft.core.fluids.ViscousFluid.eta_f` or to `osaft.core.fluids.ViscoelasticFluid.eta_f`
`zeta_f`	Wraps to `osaft.core.fluids.ViscousFluid.zeta_f` or to `osaft.core.fluids.ViscoelasticFluid.zeta_f`
`k_f`	Wraps to `osaft.core.fluids.ViscousFluid.k_f` or to `osaft.core.fluids.ViscoelasticFluid.k_f`
`k_v`	Wraps to `osaft.core.fluids.ViscousFluid.k_v` or to `osaft.core.fluids.ViscoelasticFluid.k_v`
`delta`	Wraps to `osaft.core.fluids.ViscousFluid.delta` or to `osaft.core.fluids.ViscoelasticFluid.delta`
`lambda_v`	Wraps to `osaft.core.fluids.ViscousFluid.lambda_v` or to `osaft.core.fluids.ViscoelasticFluid.lambda_v`
`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`

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`	Wraps to `osaft.core.backgroundfields.BackgroundField.wave_type`

Inherited from BaseScattering

N_max

Cutoff mode number for infinite sums

Public Methods:

`radial_particle_displacement`(r, theta, t[, mode])	First-order radial particle displacements [m]
`radial_particle_velocity`(r, theta, t[, mode])	First-order radial particle velocity [m/s]
`tangential_particle_displacement`(r, theta, t)	First-order tangential particle displacements [m]
`tangential_particle_velocity`(r, theta, t[, mode])	First-order tangential particle displacements [m]
`potential_coefficient`(n)	Wrapper to the fluid scattering coefficients for an inviscid fluid
`a`(n)	Coefficient \(a_n\) [m^2/s]
`a_hat`(n)	Coefficient \(\hat{a}_n\) [m^2/s]
`b`(n)	Coefficient \(b_n\) [m^2/s]
`b_hat`(n)	Coefficient \(\hat{b}_n\) [m^2/s]
`V_r_sc`(n, r)	Scattering contribution to \(V_{rn}(r)\) [m/s]
`d_V_r`(n, r, scattered, incident)	\(\partial_r V_{rn}(r)\) [m/s]
`d_V_r_sc`(n, r)	\(\partial_r V_{rn}^{sc}(r)\) [m/s]
`d_V_r_i`(n, r)	\(\partial_r V_{rn}^{i}(r)\) [m/s]
`d2_V_r`(n, r, scattered, incident)	\(\partial^2_r V_{rn}(r)\) [m/s]
`d2_V_r_i`(n, r)	\(\partial^2_r V_{rn}^{i}(r)\) [m/s]
`d2_V_r_sc`(n, r)	\(\partial^2_r V_{rn}^{sc}(r)\) [m/s]
`V_theta_sc`(n, r)	Scattering contribution to \(V_{\theta n}(r)\) [m/s]
`d_V_theta`(n, r, scattered, incident)	\(\partial_r V_{\theta n}(r)\) [m/s]
`d_V_theta_sc`(n, r)	\(\partial_r V_{\theta n}^{sc}(r)\) [m/s]
`d_V_theta_i`(n, r)	\(\partial_r V_{\theta n}^{i}(r)\) [m/s]
`d2_V_theta`(n, r, scattered, incident)	\(\partial^2_r V_{\theta n}(r)\) [m/s]
`d2_V_theta_sc`(n, r)	\(\partial^2_r V_{\theta n}^{sc}(r)\) [m/s]
`d2_V_theta_i`(n, r)	\(\partial^2_r V_{\theta n}^{i}(r)\) [m/s]
`phi`(n, r, scattered, incident)	\(\varphi_n(r)\)
`phi_sc`(n, r)	\(\varphi_n^{sc}(r)\)
`phi_i`(n, r)	\(\varphi_n^i(r)\)
`d_phi`(n, r, scattered, incident)	\(\partial_r \varphi_n(r)\)
`d_phi_sc`(n, r)	\(\partial_r \varphi_n^{sc}(r)\)
`d_phi_i`(n, r)	\(\partial_r \varphi_n^{i}(r)\)

Inherited from CoefficientMatrix

`det_M_n`(n[, column])	Determinant of the matrix M for the mode n
`matrix_M`(n)	Matrix \(M_l\)
`vector_n`(n)	Vector \(n_l\)
`viscosity_term`()	Often used function of fluids shear and bulk viscosity
`a_0`()	Coefficient \(a_0\) [m^2/s]
`a_hat_0`()	Coefficient \(\hat{a}_0\) [m^2/s]
`D_0`()	Coefficient \(D_0\)

Inherited from BaseDoinikov

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 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

D_0()

Coefficient \(D_0\)

(Eq. A17)

Returns: coefficient D_0

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)[source]

Scattering contribution to \(V_{rn}(r)\) [m/s]

(Eq. 35)

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)[source]

Scattering contribution to \(V_{\theta n}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

a(n)[source]

Coefficient \(a_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
Return type: complex
Returns: coefficient a_n

a_0()

Coefficient \(a_0\) [m^2/s]

(Eq. A15)

Returns: coefficient a_0

a_hat(n)[source]

Coefficient \(\hat{a}_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
Return type: complex
Returns: coefficient a_hat_n

a_hat_0()

Coefficient \(\hat{a}_0\) [m^2/s]

(Eq. A15)

Returns: coefficient a_0

b(n)[source]

Coefficient \(b_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
Return type: complex

b_hat(n)[source]

Coefficient \(\hat{b}_n\) [m^2/s]

(Eq. A18)

Parameters: n (int) – mode
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

d2_V_r(n, r, scattered, incident)[source]

\(\partial^2_r V_{rn}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d2_V_r_i(n, r)[source]

\(\partial^2_r V_{rn}^{i}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d2_V_r_sc(n, r)[source]

\(\partial^2_r V_{rn}^{sc}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d2_V_theta(n, r, scattered, incident)[source]

\(\partial^2_r V_{\theta n}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d2_V_theta_i(n, r)[source]

\(\partial^2_r V_{\theta n}^{i}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d2_V_theta_sc(n, r)[source]

\(\partial^2_r V_{\theta n}^{sc}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_r(n, r, scattered, incident)[source]

\(\partial_r V_{rn}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d_V_r_i(n, r)[source]

\(\partial_r V_{rn}^{i}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_r_sc(n, r)[source]

\(\partial_r V_{rn}^{sc}(r)\) [m/s]

(Eq. 35)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_theta(n, r, scattered, incident)[source]

\(\partial_r V_{\theta n}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d_V_theta_i(n, r)[source]

\(\partial_r V_{\theta n}^{i}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_V_theta_sc(n, r)[source]

\(\partial_r V_{\theta n}^{sc}(r)\) [m/s]

(Eq. 36)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_phi(n, r, scattered, incident)[source]

\(\partial_r \varphi_n(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

d_phi_i(n, r)[source]

\(\partial_r \varphi_n^{i}(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

d_phi_sc(n, r)[source]

\(\partial_r \varphi_n^{sc}(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

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]

matrix_M(n)

Matrix \(M_l\)

(Eq. A19 - A 22)

Parameters: n (int) – mode
Return type: ndarray

phi(n, r, scattered, incident)[source]

\(\varphi_n(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]
scattered (bool) – scattered field
incident (bool) – incident field

Return type

complex

phi_i(n, r)[source]

\(\varphi_n^i(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

phi_sc(n, r)[source]

\(\varphi_n^{sc}(r)\)

(Eq. 28, 30)

Parameters

n (int) – mode
r (float) – radial coordinate [m]

Return type

complex

potential_coefficient(n)[source]

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)[source]

First-order radial particle displacements [m]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

Returns

first-order radial particle displacement

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

First-order radial particle velocity [m/s]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

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)[source]

First-order tangential particle displacements [m]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

Returns

first-order tangential particle displacements

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

First-order tangential particle displacements [m]

Parameters

r (float | Sequence) – radial coordinate [m]
theta (float | Sequence) – tangential coordinate [rad]
t (float | Sequence) – time [s]
mode (None | int, optional) – mode
Default: None

Return type

complex | NDArray

Returns

first-order tangential particle displacements

vector_n(n)

Vector \(n_l\)

(Eq. A19 - A 22)

Parameters: n (int) – mode
Return type: ndarray

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