pyGCS 0.2.1

A package to establish grid independent results for numerical analysis on computational grids.

Introduction

pyGCS (Grid Convergence Study) is a python package that calculates the Grid Convergence Index (GCI) for solutions obtained through numerical analysis using computational grids to establish the error-band of the solution with respect to the numerical grid used. This package implements the equations presented in [1] and [2].

Installation

To install pyCGS, run the following command

pip3 install pycgs

Usage

The following shows how to calculate the GCI and get additional information that may be useful to establish grid independence.

import pyGCS

# number of cells per grid
grids = [18000, 8000, 4500]

# volume of the simulation domain for each simulation
volume = [76, 76, 76]

# integral quantity for which to calculate the GCI
solution = [6.063, 5.972, 5.863]

# dimension of the simultion (here 2D)
dimension = 2

# create GCI object
grid_convergence_study = pyGCS.GCI(dimension, volume, grids, solution)

# get GCI and supporting information
gci = grid_convergence_study.get_gci()
asymptotic_gci = grid_convergence_study.get_asymptotic_gci()
order = grid_convergence_study.get_order()

# GCI_32 = 4.11%
print('GCI for coarse to medium grid (GCI_32): ' + str(gci[1] * 100) + '%')

# GCI_21 = 2.17%
print('GCI for medium to fine   grid (GCI_21): ' + str(gci[0] * 100) + '%')

# asymptotic GCI = 1.015
print('asymptotic GCI value (a value close to 1 indicates grid independence): ' + str(asymptotic_gci[0]))

# order = 1.53
print('order achieved in simulation: ' + str(order[0]))

References

1. Celik et al. "Procedure of Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications", Journal of Fluids Engineering, 130(7), 2008
2. https://www.grc.nasa.gov/www/wind/valid/tutorial/spatconv.html