edg_acoustics.boundary_condition

This module provides boundary condition functionalities for the edg_acoustics package.

The edg_acoustics.boundary_condition provide more necessary functionalities (based upon edg_acoustics.acoustics_simulation) to setup boundary condition for a specific scenario.

Please note that most of used mesh functions and classes in edg_acoustics are present in the main edg_acoustics namespace rather than in edg_acoustics.boundary_condition.

Todo

  • For future development, the module can be extended to include other types of boundary conditions.

  • maybe add flux boundary conditions.

Module Contents

Classes

BoundaryCondition

Abstract base class for boundary conditions.

AbsorbBC

Setup absorptive boundary condition of a DG acoustics simulation for a specific scenario.

Attributes

FREQ_MAX

maximum resolvable frequency.
edg_acoustics.boundary_condition.FREQ_MAX = 2000.0[source]

maximum resolvable frequency.

Type:

float

class edg_acoustics.boundary_condition.BoundaryCondition[source]

Bases: abc.ABC

Abstract base class for boundary conditions.

static init_ADEvariables(BCpara, BCnode)[source]

Initiate ADE variables, normal velocity, characteristic waves (outgoing and incoming).

Parameters:
Returns:

BCvar (list [dict]) – see edg_acoustics.AbsorbBC.BCvar.

static check_BCpara(BCnode, BCpara, freq_max)[source]

Check if BCpara is compatible with AcousticsSimulation.BCnode and satisfies physical admissibility condition.

Given an acoustics simulation data structure with a set of boundary conditions specified in acoustics_simulation.BCnode, check if the list of boundary conditions specification and parameters are compatible. By compatible we mean that all boundary conditions (keys) in BCpara exist in acoustics_simulation.BCnode, and vice-versa. Also, to satisfy the causality and reality conditions, multi-pole model parameters \(\zeta_i\) (stored in first row of numpy.array BCpara[BC_label] need to be positive. To satisfy the passivity condition, the magnitude of the reflection coefficient from the multi-pole model need to be smaller than 1, that is, \(|R(\omega)|\leq 1\), where

\[R(\omega)\approx{R}_\infty+\sum_{k=1}^{S}\frac{A_k}{\zeta_k+\mathrm{i}\omega}+ \sum_{l=1}^{T} \frac{1}{2}\Big( \frac{B_l-\mathrm{i}C_l}{\alpha_l-\mathrm{i}\beta_l+\mathrm{i}\omega}+\frac{B_l+\mathrm{i}C_l}{\alpha_l+\mathrm{i}\beta_l+\mathrm{i}\omega} \Big)\]
Parameters:
Raises:

  • AssertionError – If BCpara.[index][‘label’] is not present in the acoustics_simulation.BCnode.[index][‘label’], an error is raised. If a label is present in the acoustics_simulation.BCnode.[index][‘label’] but not in BCpara, an error is raised. If the labels in BCpara and BCnode are not the same, an error is raised.

  • AssertionError – If the reflection coefficient is not smaller than 1, an error is raised.

  • AssertionError – If the number of BC types is not the same in the BC_labels and BC_para, an error is raised.

  • AssertionError – If the causality and reality conditions are not met, an error is raised.

static compute_Re(omega, paras)[source]

Computes the reflection coefficient given the passed parameter of the multi-pole model at the frequencies of omega.

Parameters:
Returns:

Re (numpy.ndarray) – reflection coefficient at the frequencies of omega.

class edg_acoustics.boundary_condition.AbsorbBC(BCnode, BCpara, freq_max=FREQ_MAX)[source]

Bases: BoundaryCondition

Setup absorptive boundary condition of a DG acoustics simulation for a specific scenario.

AbsorbBC is used to load the boundary condition parameters, and to initiate the ADE variables.

Parameters:
BCpara

a list of boundary conditon parameters from the multi-pole model. Each element is a dictionary with keys (values) [‘label’(int),’RI’(float),’RP’(numpy.ndarray),’CP’(numpy.ndarray)]. ‘RI’ refers to the limit value of the reflection coefficient as the frequency approaches infinity, i.e., \(R_\infty\). ‘RP’ refers to real pole pairs, i.e., \(A\) (stored in 1st row), \(\zeta\) (stored in 2nd row). ‘CP’ refers to complex pole pairs, i.e., \(B\) (stored in 1st row), \(C\) (stored in 2nd row), \(\alpha\) (stored in 3rd row), \(\beta\) (stored in 4th row).

More details about the multi-pole model parameters and boundary condition can be found in reference https://doi.org/10.1121/10.0001128.

BCpara[:][‘label’] must contain the same integer elements as acoustics_simulation.BCnode[:][‘label’], i.e., all boundary conditions in the simulation must have an associated boundary condition parameters.

Type:

list [dict]

BCvar

a list of ADE variables. Each element corresponds to one type of BC, and is a dictionary with potential keys [‘label’, ‘vn’, ‘ou’, ‘in’, ‘phi’, ‘PHI’, ‘kexi1’, ‘kexi2’, ‘KEXI1’, ‘KEXI2’].

Type:

list [dict]