Richardson extrapolation

Perspective (graphical)

Calculus (dental)

Mathematics

Economic growth

Algorithm

Statistics

Mathematical optimization

Extrapolation

Epistemology

Philosophy

Estimator

Artificial intelligence

Economics

Grid

Dentistry

Geometry

Convergence (economics)

Computer science

Simple (philosophy)

A priori and a posteriori

Applied mathematics

Medicine

Journal of Fluids Engineering

This paper proposes the use of a Grid Convergence Index (GCI) for the uniform reporting of grid refinement studies in Computational Fluid Dynamics. The method provides an objective asymptotic approach to quantification of uncertainty of grid convergence. The basic idea is to approximately relate the results from any grid refinement test to the expected results from a grid doubling using a second-order method. The GCI is based upon a grid refinement error estimator derived from the theory of generalized Richardson Extrapolation. It is recommended for use whether or not Richardson Extrapolation is actually used to improve the accuracy, and in some cases even if the conditions for the theory do not strictly hold. A different form of the GCI applies to reporting coarse grid solutions when the GCI is evaluated from a “nearby” problem. The simple formulas may be applied a posteriori by editors and reviewers, even if authors are reluctant to do so.

Perspective: A Method for Uniform Reporting of Grid Refinement Studies