Acoustic analogy (ACA)

When using the ACA solver the workflow usually consists of three steps

1. Generating input describing temporal series on a FWH permeable surface
   1. Generating a surface grid and gathering data during a simulation run such as the FV, LB, or DG solver on this surface grid
   2. By describing the source term via an analytical function such as Mono-, Di-, or Quadropole by the ACA solver itself
2. Far-Field prediction for specified observer locations using the ACA solution methods
3. Optionally post-process output at observer location which is dumped in time as well as in frequency domain. All post-processing related to the ACA solver is possible to be run directly after step 2.

In the following these three steps are given in details.
A detailed overview of all possible properties is given here.

Generating input

Using sampled data from a previous solver run

To generate input data to be solved with the FWH method at first a FWH permeable surface needs to be defined. This is done by providing a triangulated surface geometry written in an ASCII .stl file format. These file may be generated using a python script, paraview, or an external meshing tool. It is possible that the surface is distributed among multiple files. Assuming in the following these files are named fwh0.stl, fwh1.stl and so forth.

To sample flow or acoustic field data in the previous solver run the post processing needs to be enabled to activate the surface sampling options

#..stuff relevant for the FV, LB, or DG solver run..
 
# The following block is described in post processing page
solvertype.1                = "MAIA_POST_DATA"
geometryInputFileName.1     = "geometry.toml"
outputDir.1                 = "out_surfaceSampling/"
solvertype.1                = "POST_DATA"
postprocessingOrder_0       = [0,1]
noPostProcessing            = 1
postProcessingSolverIds     = [0]
postProcessingType_0        = "POSTPROCESSING_LB"
 
# Enable the surface sampling post processing operation
postProcessingOps_0         = ["PP_SURFACE_SAMPLING_IN"]
 
# Configure sampling properties
surfaceDataStartTimeStep    = 396800    # Start time step of sampling
surfaceDataEndTimeStep      = 1984000   # End time step of sampling
surfaceDataSampleInterval   = 64        # Interval of sampling data
surfaceDataWriteInterval    = 9920      # Interval of writing data in a sampled file
 
# Name of the surface/s to be considered for sampling
surfaceDataFileName_0       = "stl/fwh0.stl"
surfaceDataFileName_1       = "stl/fwh1.stl"

Here, every 9920 time steps for each of the two surfaces a surface sample file is written. Each of these files contains surfaceDataWriteInterval/surfaceDataSampleInterval = 155 temporal samples for each triangle defined in the surfaceDataFileName geometry. Thus, at the end per each surface data (surfaceDataEndTimeStep-surfaceDataStartTimeStep)/surfaceDataWriteInterval=160 sampled files are located in the directory out_surfaceSampling/. The first file will be named with the suffix id number surfaceDataStartTimeStep/surfaceDataWriteInterval = 40, i.e., the number starts from the first time step even if later sampling start time step is chosen.

Using analytical input function

The generation of analytical input data is done right in advance of a simulation run. This is documented here in the following section.

Far-field prediction

To predict the acoustic far-field using the ACA solver three steps are relevant for setting up a case

1. Choose the numerical method see here for more background information
2. Specify your input data of the FWH permeable surface
3. Set boundary conditions, if necessary
4. Define the observer points of interest
5. (Choose relevant post-processing routine, described in the next section)

In the following the different parts of a ACA property file are described individually, whereas a merged file is given here in advance:

(Click here to expand complete property file)

More options and details about different types, e.g. for windowType, are documented here.

#-------------------------------------------------------------------------------
#---GENERAL---------------------------------------------------------------------
#-------------------------------------------------------------------------------
# This part deals with general properties described previously in the documention.
 
#---APPLICATION SETTINGS--------------------------------------------------------
flowSolver                        = True
gridGenerator                     = False
 
#---FLOW VARIABLES--------------------------------------------------------------
Ma                                = [0.1, 0.0, 0.0]
 
#---I/O-------------------------------------------------------------------------
outputDir.default                 = "./out_fwh/"
 
#---NUMERICAL PROPERTIES--------------------------------------------------------
nDim                              = 3
noSolvers                         = 1
 
executionRecipe                   = "RECIPE_BASE"
solvertype.default                = "MAIA_UNIFIED"
 
#---SOLUTION PROPERTIES---------------------------------------------------------
timeSteps                         = 1
solutionInterval                  = -1
residualInterval                  = -1
 
#---MEMORY----------------------------------------------------------------------
scratchSize                       = 25.0
maxNoCells                        = 1000000                 # required by m-AIA for total scratch size
 
#-------------------------------------------------------------------------------
#---ACA (FWH)-------------------------------------------------------------------
#-------------------------------------------------------------------------------
# This part deals with the properties relevant for the ACA solver using the FWH method
 
#---1. NUMERICAL PROPERTIES-----------------------------------------------------
solvertype.0                      = "MAIA_ACOUSTIC_ANALOGY" # Choosing the ACA solver
acousticMethod                    = "FWH"                   # Choosing the FWH method
transformationType                = 1                       # Here, 1: Fast-Fourier transformation
windowType                        = 3                       # Type of the window function. Here, 3: Hamming
 
#---2. Input data---------------------------------------------------------------
# To deal with input from different solvers a unit conversion step might be
# performed in advance of solving the FWH. The format of this conversion is
# defined by the acaResultsNondimMode property. Also, this property handles the
# form of the output units. For more reference it is referred to the property
# page of the ACA solver.
acaResultsNondimMode              = 2                       # Here, 2: LB input and Infty State output 
 
#--input: from sampling data
generateSurfaceData               = False                   # Disabling the analytical source term generation
 
useMergedInputFile                = False                   # If all sample files are merged together
inputDir                          = "./out_surfaceSampling/" # Directory where sample files are located
noSurfaces                        = 2                       # Number of FWH permeable surfaces
surfaceIds                        = [0,1]                   # Ids of the FWH permeable surface sample files
 
# NOTE:
# The number of samples should be a potency of 2. Otherwise no FFT can be used
# and computation is slowed down heavily.
# Here, each file contains 155 temporal samples
inputFileIndexStart               = [94]                    # Sample file index start
inputFileIndexEnd                 = [200]                   # Sample file index end
acaNoSamples                      = 16384                   # Number of temporal samples that shall be used
 
 
 
# #--input: from analytical function
# # Alternativ: Input is prescribed by analytical source term as discussed in
# # the previous section
# generateSurfaceData           = True                        # Enabling the analytical source term generation
# generateSurfaceDataNoSamples  = 64                          # Number of surface data samples to be generated
# #- Description of the analytical source term
# sourceType                    = 2                           # Type of source term (Here, 2 = Quadrupole)
# omega_factor                  = 2                           # Omega = pi * c_infty * omega_factor
# noPeriods                     = 8.3                         # Number of periods. Default = 1
# dimless                       = True                        # Generation of sound source without dimensions
# #- Description of the FWH permeable surfaces
# noSurfaces                    = 2                           # Number of FWH permeable surfaces to created
# # First FWH permeable surface
# surfaceType_0                 = 0                           # Geometry type of the surface (Here, 0 = plane)
# surfaceNormalDir_0            = 0                           # Surface normal dir (Here, 0 = -x direction)
# surfaceCoordinates_0          = [-3.0, -3.0, -3.0, -3.0, 3.0, 3.0 ] # Box of the plane [-x.-y.-z, +x,+y,+z]
# noSegments_0                  = [0, 40, 40]                 # Number segments in each Cartesian direction
# # Second FWH permeable surface
# surfaceType_1                 = 0
# surfaceNormalDir_1            = 1                           # Surface normal dir (Here, 1 = +x direction)
# surfaceCoordinates_1          = [3.0, -3.0, -3.0, 3.0, 3.0, 3.0]
# noSegments_1                  = [0, 40, 40]
 
#---3. Observer points----------------------------------------------------------
#--observer location: from .csv file
generateObservers                 = False                   # Generate observer (True) or use observerFile (False)
observerFileName                  = "observerLocation.csv"  # .csv file with observer point coordinates
 
# #--observer location: distribute observer points along a circular path
# # Alternative: Generate observer points, instead of using a .csv input file
# generateObservers                 = True
# observerRadius                    = 10.0                    # Radius of the circlular path
# noObservers                       = 100                     # Number of observer points generated
 
#---4. boundary condition---------------------------------------------------
# # Here, two symmetry planes are set, with normal in +y and in +z direction.
# symmetryOrigin = [0.0, 0.0, 0.0,                            # Origin of plane 1
#                   0.0, 0.0, 0.0 ]                           # Origin of plane 2
# symmetryNormal = [0.0, 0.0, 1.0,                            # Normal of plane 1
#                   0.0, 1.0, 0.0 ]                           # Normal of plane 2
 
#---5. ACA SPECIFIC POST PROCESSING---------------------------------------------
# The following is presented in the next section in more details
acaPostprocessingMode             = False                   # Apply after run (False), or on data already generated (True)
noPostprocessingOps               = 2                       # Number of post processings operations to be used
postprocessingOps                 = [0, 2]                  # Here, 0:RMS of pressure, 2: SPL

Numerical methods

#---1. NUMERICAL PROPERTIES-----------------------------------------------------
solvertype.0                      = "MAIA_ACOUSTIC_ANALOGY" # Choosing the ACA solver
acousticMethod                    = "FWH"                   # Choosing the FWH method
transformationType                = 1                       # Here, 1: Fast-Fourier transformation
windowType                        = 3                       # Type of the window function. Here, 3: Hamming

The name of the solver is MAIA_ACOUSTIC_ANALOGY, which features an acousticMethod in the moment named "FWH" (see mathematical model and numerical method). As the FWH equation is solved in frequency domain and sampled input data and some of the output data is in time domain a transformation (here Fourier transformation) between these domains is required and set via transformationType. A Fourier transformation requires an infinite long temporal sample. Hence, spectral leakage may occur when using a restricted input signal length. This is reduced by choosing an appropriate windowing function via windowType.

Input data of FWH permeable surface

Data can be made non-dimensional in different ways. Therefore, the flag acaResultsNondimMode is used to specify different modes of assuming input data dimensions and writing output data with a certain dimension. E.g., the mode 2 assumes that the input data is made non-dimensional as done in the LB solver while the output is made non-dimensional by the infinity state as described in the numerical method of the ACA solver.

#---2. Input data---------------------------------------------------------------
# To deal with input from different solvers a unit conversion step might be
# performed in advance of solving the FWH. The format of this conversion is
# defined by the acaResultsNondimMode property. Also, this property handles the
# form of the output units. For more reference it is referred to the property
# page of the ACA solver.
acaResultsNondimMode              = 2                       # Here, 2: LB input and Infty State output 

As already outlined in the generating input section different ways of defining/reading input data are possible.

To read input from sampling files obtained from a previous solver run as described in generating input the following set of properties is relevant

#--input: from sampling data
generateSurfaceData               = False                   # Disabling the analytical source term generation
 
useMergedInputFile                = False                   # If all sample files are merged together
inputDir                          = "./out_surfaceSampling/" # Directory where sample files are located
noSurfaces                        = 2                       # Number of FWH permeable surfaces
surfaceIds                        = [0,1]                   # Ids of the FWH permeable surface sample files
 
# NOTE:
# The number of samples should be a potency of 2. Otherwise no FFT can be used
# and computation is slowed down heavily.
# Here, each file contains 155 temporal samples
inputFileIndexStart               = [94]                    # Sample file index start
inputFileIndexEnd                 = [200]                   # Sample file index end
acaNoSamples                      = 16384                   # Number of temporal samples that shall be used

In the case where multiple data on multiple surfaces is sampled, these are selected using noSurfaces and the corresponding Id via surfaceIds.
It is possible to use only a subset of the sampling files controlled via the properties inputFileIndexStart and inputFileIndexEnd. Furthermore, the number of temporal samples read from these files is controlled via acaNoSamples.

Note

useMergedInputFile = True

Using this property requires the usage of a python script located in the m-AIA tools repository. With this it's possible to merge multiple sample files into a single file in advance of an ACA solver run.

Input from an analytical function is possible by considering two steps. First, a function describing the acoustic sources is to be selected. Second, the shape of the used FWH permeable surface/s needs to be described.
The source term type is choosen via sourceType, whereas it's frequency, signal length, and units are controlled via the following properties

#--input: from analytical function
# Alternativ: Input is prescribed by analytical source term as discussed in
# the previous section
generateSurfaceData           = True                        # Enabling the analytical source term generation
generateSurfaceDataNoSamples  = 64                          # Number of surface data samples to be generated
#- Description of the analytical source term
sourceType                    = 2                           # Type of source term (Here, 2 = Quadrupole)
omega_factor                  = 2                           # Omega = pi * c_infty * omega_factor
noPeriods                     = 8.3                         # Number of periods. Default = 1
dimless                       = True                        # Generation of sound source without dimensions

Multiple number of discrete FWH permeable surface/s might be defined using the following

#- Description of the FWH permeable surfaces
noSurfaces                    = 2                           # Number of FWH permeable surfaces to created
# First FWH permeable surface
surfaceType_0                 = 0                           # Geometry type of the surface (Here, 0 = plane)
surfaceNormalDir_0            = 0                           # Surface normal dir (Here, 0 = -x direction)
surfaceCoordinates_0          = [-3.0, -3.0, -3.0, -3.0, 3.0, 3.0 ] # Box of the plane [-x.-y.-z, +x,+y,+z]
noSegments_0                  = [0, 40, 40]                 # Number segments in each Cartesian direction
# Second FWH permeable surface
surfaceType_1                 = 0
surfaceNormalDir_1            = 1                           # Surface normal dir (Here, 1 = +x direction)
surfaceCoordinates_1          = [3.0, -3.0, -3.0, 3.0, 3.0, 3.0]
noSegments_1                  = [0, 40, 40]

Boundary conditions

For certain problems the usage of a symmetry boundary might be useful if the sampled data is not available. Therefore, a symmetry plane is defined by a point (symmetryOrigin) and a surface normal (symmetryNormal). For usage of multiple planes these two properties are simply continued

# Here, two symmetry planes are set, with normal in +y and in +z direction.
symmetryOrigin = [0.0, 0.0, 0.0,                            # Origin of plane 1
                  0.0, 0.0, 0.0 ]                           # Origin of plane 2
symmetryNormal = [0.0, 0.0, 1.0,                            # Normal of plane 1
                  0.0, 1.0, 0.0 ]                           # Normal of plane 2

Definition of observer points

The location of the observer points is described either via a .csv file or by using an analytical description, flagged by the property generateObservers.
The location of the .csv file is given with

#--observer location: from .csv file
generateObservers                 = False                   # Generate observer (True) or use observerFile (False)
observerFileName                  = "observerLocation.csv"  # .csv file with observer point coordinates

Here, observerLocation.csv might look as following, defining two arbitrarily located observer points

1.00001 10.0  -2.0
20.0    10.0  -2.0

To generate observer points distributed along a circular path an observerRadius as well as a noObservers needs to be given

#--observer location: distribute observer points along a circular path
# Alternative: Generate observer points, instead of using a .csv input file
generateObservers                 = True
observerRadius                    = 10.0                    # Radius of the circlular path
noObservers                       = 100                     # Number of observer points generated

Post-processing

Different post processing operations are provided by the ACA solver, which might be applied directly after the solver run, or in a post-step on observer data already generated using the post processing mode (acaPostprocessingMode = True). The number of post processing operations (noPostprocessingOps) and the type of the postprocessingOps is given here for an example

#---5. ACA SPECIFIC POST PROCESSING---------------------------------------------
# The following is presented in the next section in more details
acaPostprocessingMode             = False                   # Apply after run (False), or on data already generated (True)
noPostprocessingOps               = 2                       # Number of post processings operations to be used
postprocessingOps                 = [0, 2]                  # Here, 0:RMS of pressure, 2: SPL

all operations available are documented in the ACA property page.