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 Engineering-Transactions 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:

grid-convergence /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:

grid-convergence /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/.