Comparison of Discrete and Continuous Shape Derivatives

Modification of the helmholtz-x repository for the purpose of computing of discrete shape derivatives on the acoustic duct, Rijke tube and Kornilov case.

• Compute continuous, discrete and analytic shape derivatives
• Build figures

Structure the repository:

• /helmholtz_x: contains a slightly modified version of the HelmholtzX toolbox
• /RijkeTube: 2D Rijke tube geometry test case
• /KornilovCase: Kornilov geometry test case
• /Figures: building datasets and plotting figures and results

Use paraview to analyse .xdmf files within:

• /Meshes: contains mesh files
• /Results: direct and adjoint eigenvectors and eigenvalues as .txt file
• /InputFunctions: h,w,T,rho,c functions and Free-Form-Deformation field Vffd
• /FTFMatrices: data for Kornilov Flame Transfer Function in state space format

The environ.yml is used to set up conda environment as explained below.
The requirements.txt file contains the required dependencies for the docker as explained below.
The main class is test_case.py, which builds and computes the requested test case.
The standard physical and computational parameters for the test cases are specified in *params.py.

Overview of the helmholtzX utilities:

• acoustic_matrices.py: assemble matrices A,B,C for discrete Helmholtz Equation: A+wB+w**2C=D(w)
• distribute_params.py: functions to distribute parameters onto the mesh file
• dolfinx_utils.py: utils for assembly of flame matrix
• eigensolvers.py: contains Newton solver for eigenvalue problem using eps solver
• eigenvectors.py: normalizations for eigenvectors
• flame_matrices.py: assemble matrix D(w)
• flame_transfer_function.py: defines FTF as n-tau model or state-space model
• io_utils.py: read and write functions
• parameter_utils.py: convert temperature, sound speed and gamma functions
• petsc4py_utils.py: vector and matrix computation methods
• shape_derivatives.py: functions to compute continuous shape derivative
• solver_utils.py: logging utilities

To set up the code on your machine follow these steps:
Quick install the suitable conda environment using the environ.yml file with the command:
~$ conda env create -f environ.yml
Then activate with:
~$ conda activate helmholtzx-env
Create subfolders called "/Meshes", "/Results", "/InputFunctions" within each testcase folder:
~$ mkdir KornilovCase/{Meshes,Results,InputFunctions} RijkeTube/{Meshes,Results,InputFunctions}
Also add the helmholtz-x-TFD directory to python path by adding this command
export PYTHONPATH="${PYTHONPATH}:/.../helmholtz-x-TFD" in your ~/.bashrc file, where you replace /... with the path to your directory.

Produce all data at once: ./runAll.sh.
Or run individually:
To test the computations, head to the corresponding folder:
~$ cd KornilovCase or ~$ cd RijkeTube
For shape derivative using continuous formula run:
~$ python3 continuous_shape_derivative_*
For shape derivative using discrete formula run:
~$ python3 discrete_shape_derivative_*
Adjust parameters in the *params.py files if needed or directly when building the object from class test_case.py.

To examine the input functions h,w,T,rho,c and the free form deformation field, run the function write_input_function() and examine .xdmf files using paraview.

To access, modify and print figures from the data_fig*.txt files with the jupyter notebooks Fig*.ipynb, use this link to create an isolated browser environment:
(loading might take a while)
Changes made in this environment will not apply to the repository and will get lost when closing the browser session.

Also, to reproduce the figure data from scratch, you can run build_data_fig*.py.
It computes the test case and save the data as data_fig* files.

Additionally, there are figures from dynX in the dynxFigures subfolder.
The dynx_data_fig*.txt are created within the dynX repository.