Approximate Error Spline (AES) Method for Grid Convergence Error Estimate
Many times it is difficult to determine if your simulation is grid independent. This is especially the case if your are seeing oscillatory convergence. The AES method has been found to provide better estimates of the grid convergence error than the usual Richardson Extrapolation technique. This method was developed by Celik et. al. The papers that were used to develop the excel program are:
Celik, I., & Li, J. (n.d.). Assesment of Numerical Uncertainty for the Calculations of Turbulent Flow over a Backward-Facing Step. Int. J. Numer. Meth. Fluids, 49, 1015–1031.
Celik, I., Li, J., Hu, G., & Shaffer, C. (n.d.). Limitations of Richardson Extrapolation and Some Possible Remedies. J. Fluids Eng., 127, 795–805.
The excel program developed by Vivid Numerics Inc. is available for download here:AES method.xls
The method requires that the user enter the volume of the simulation domain at each grid level (Should be the same), the number of cells at each grid, the number of spatial dimensions (usually 2 or 3) and finally the flow or stress parameter that the user is interested in. This may be velocity, pressure, von Mises stress, a principal stress, a displacement, etc. The program then provides an estimate of the error for each grid result and an estimated true value. As with any program this one should be used with care and not followed blindly. Problems in the mesh (sliver cells, inverted cells) or in the setup may produce spurious results with this program.
The information presented in this entry is for information only. Any use of this information is at the readers/users own risk. Vivid Numerics Inc. and its owners and employees assume no responsibility if this information is implemented and the results are used for any critical or non-critical studies or analyses.