BaseScatteringDoinikov1994

Examples using this class are:

Frontiers: Copper Particle in Viscous Oil

Doinikov Rigid (1994): Sandstone in Glycerin

Pressure Plots for different theories

Doinikov 1994 Models

Possible Numerical Problems

class osaft.solutions.basedoinikov1994.scattering.BaseScatteringDoinikov1994(N_max)[source]

Bases: BaseScattering, ABC

Base scattering class for Doinikov solutions from 1994

Parameters: N_max (int) – Highest order mode included in the computation [-]

Public Data Attributes:

`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

Public Methods:

`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`

abstract A_in(n)[source]

Incoming wave amplitude

Parameters: n (int) – mode

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]

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)[source]

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

abstract alpha_n(n)[source]

\(\alpha_n\) coefficient

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

abstract beta_n(n)[source]

\(\beta_n\) coefficient

Parameters: n (int) – mode
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)

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

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

Returns the value for the radial particle 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]
mode (None | int, optional) – specific mode number of interest; if None then all modes until 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

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

Returns the value for the tangential particle 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]
mode (None | int, optional) – specific mode number of interest; if None then all modes until 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()

abstract property k_f: complex

Returns the wave number in the fluid \(k_f\) [1/m]

Return type: complex

abstract property k_v: complex

Returns the viscous wave number in the fluid \(k_v\) [1/m]

Return type: complex