A Python program to Perform Calculations Associated with a Grid Convergence Study
Project description
convergence
A Python program to Perform Calculations Associated with a Grid Convergence Study.
Introduction
This is a port of verify.f90, a program provided as part of the NASA Examining Spatial (Grid) Convergence tutorial.
http://www.grc.nasa.gov/WWW/wind/valid/tutorial/spatconv.html
Additional changes have been made to reflect the recommendations in:
Celik, I. B., Ghia, U., & Roache, P. J. (2008). Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. Journal of fluids EngineeringTransactions of the ASME, 130(7).
This code was written by Mathew Topper between 2009 and 2011 as part of the Supergen Marine Research Consortium project. I was younger then and would do many things differently now. I am working on updating this code to make the main class and functions more easy to use and also integrate into other projects. Watch this space.
Installation
The package requires no dependencies and is currently available for Pythons 2.7, 3.5, 3.6, 3.7 and 3.8.
The package can be installed by downloading the source code, and using a terminal or command prompt as follows:
cd /path/to/convergence
python setup.py install
The package can also be downloaded from PyPI, again using a terminal or command prompt:
pip install convergence
Basic Usage
The package provides a command line interface which is the main (and currently only sensible) way to use the package. The input data must be a space delimeted text file with the first column being the grid spacing and the second column being the metric of interest. An example can be found in the data folder of the source code.
The program can then be executed as follows:
gridconvergence /path/to/data/file
By default, the results of the program are written to a file called verify_report.txt in the calling directory. The file name can be changed using the o or out command line options. The format of the file is as follows:
 VERIFY: Performs verification calculations 
Number of grids to be examined = 3
Grid Size Quantity
1.000000 0.970500
2.000000 0.968540
4.000000 0.961780
Discretisation errors for fine grids:
Grids  e_approx  e_extrap  f_exact  gci_coarse 
=========================================================================
1 2 3  0.002020  0.000824  0.971300  0.003555 

Grids  gci_fine  p  r21  r32 
=========================================================================
1 2 3  0.001031  1.786170  2.000000  2.000000 

Discretisation errors for coarse grids:
Grids  e_approx  e_extrap  f_exact  gci_coarse 
=========================================================================
1 2 3  0.006980  0.002842  0.971300  0.012287 

Grids  gci_fine  p  r21  r32 
=========================================================================
1 2 3  0.003562  1.786170  2.000000  2.000000 

Asympototic ratio test:
Grids  Asymptotic ratio 
====================================
1 2 3  0.997980 

 End of VERIFY 
In the first table the input data is displayed. The second table shows the fine analysis results for each trio of grids and the second table shows the coarse analysis results for each trio. The final table shows the asymptotic ratio.
The headers of the tables have the following meanings:
 Grids: the trio of grids being analysed
 e_approx: approximate relative error
 e_extrap: extrapolated relative error
 f_exact: the estimated the zero grid spacing value
 gci_coarse: coarse grid convergence index
 gci_fine fine grid convergence index
 p: order of convergence
 r21: ratio of the middle to fine grid spacing
 r32: ratio of the coarse to middle grid spacing
Known Analytical Result
If there is a known zero spacing value for the convergence study this value can be added to the analysis using the a or analytical command line option. To illustrate, the basic example would now become:
gridconvergence /path/to/data/file a 0.12345
Additional headers now appear in the fine and coarse analysis tables with the following meanings:
 e_analytic: analytical relative error
 f_analytic: the analytical the zero grid spacing value
 f_delta: the different between the analytical and estimated zero grid spacing value
License
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.
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