Order of interpolation

gravis · January 5, 2011, 09:10

Hi,

I have not managed to find any info in the CFX-12 documentation regarding how the interpolation is done when using CFX-Post in "comparison mode" to compare different meshes. Basically, I would like to know what the order of the interpolation is, and how it is carried out.

Also, I would like to know the equivalent for the CFX Solver interpolator. Is the same method of interpolation used?

Thanks,
Reine

gravis · February 17, 2011, 08:32

Since I have been in contact with the support I have learned that CFX-Post uses a trilinear interpolation of first order. Presumably, the interpolation in the solver is also of first order accuracy.

For example, imagine carrying out a grid refinement study using a second order scheme. It concerns me a bit that this first order approximation will limit the overall accuracy, if one would like to compare local quantities rather than some global variable.

Any thoughts on this?

In Celik's [1] paper on Richardson extrapolation, they use a "third order Newton's Divided Difference Polynomial" to interpolate the results between different grids. However, I have not seen the use of higher order interpolation methods elsewhere than in this paper. I would appreciate any recommendations on literature regarding methods for interpolation.

[1] Celik, I., Karatekin, O.
Numerical experiments on application of Richardson extrapolation with nonuniform grids
(1997) Journal of Fluids Engineering, Transactions of the ASME, 119 (3), pp. 584-589.

gravis · February 17, 2011, 11:07

Also, correct me if I am wrong, as I have understood a 1D linear interpolation (CDS) between two nodes of a regular grid is second order accurate. i.e. the leading truncation error term is proportional to the square of the distance between the nodes and the polynomial order is 1.

And, as I have understood, a trilinear interpolation is identical to three successive linear interpolations. Therefore, it seems to me that a trilinear interpolation (on a regular grid) should also be second order accurate.

However, at Wikipedia's page for Trilinear_interpolation it is written that:

"The order of accuracy is 1 for all these interpolation schemes" (linear, bilinear and trilinear )

Can someone clear this out for me? Is it a general statement that holds for all grid types?

ghorrocks · February 17, 2011, 22:17

Quote:

Presumably, the interpolation in the solver is also of first order accuracy.

What "interpolation" are you referring to here?

Be careful here - the interpolation for initial condition calculations or comparisons between results file is done by trilinear interpolation, but the advection discretisation is second order by default. The advection scheme is totally different to the interpolation schemes.

I think you have interpolation schemes mixed up with advection schemes.

gravis · February 18, 2011, 03:50

Hi Glenn,

Thank you for your reply.

I am only referring to the interpolation scheme, not the advection scheme.

Quote:

Originally Posted by gravis

Presumably, the interpolation in the solver is also of first order accuracy.

What I meant by this was to ask if the accuracy of the interpolation scheme in CFX-Interpolator was equal to the one used in CFD-Post in comparison mode.

Kind regards,
Reine

ghorrocks · February 18, 2011, 07:01

I think you would have to talk to CFX support for the details of the interpolators, beyond what is shown in the documentation.

January 5, 2011, 09:10	Order of interpolation	#1
gravis Member Reine Granström Join Date: Apr 2009 Location: Sweden Posts: 43 Rep Power: 17	Hi, I have not managed to find any info in the CFX-12 documentation regarding how the interpolation is done when using CFX-Post in "comparison mode" to compare different meshes. Basically, I would like to know what the order of the interpolation is, and how it is carried out. Also, I would like to know the equivalent for the CFX Solver interpolator. Is the same method of interpolation used? Thanks, Reine

February 17, 2011, 08:32	Update	#2
gravis Member Reine Granström Join Date: Apr 2009 Location: Sweden Posts: 43 Rep Power: 17	Since I have been in contact with the support I have learned that CFX-Post uses a trilinear interpolation of first order. Presumably, the interpolation in the solver is also of first order accuracy. For example, imagine carrying out a grid refinement study using a second order scheme. It concerns me a bit that this first order approximation will limit the overall accuracy, if one would like to compare local quantities rather than some global variable. Any thoughts on this? In Celik's [1] paper on Richardson extrapolation, they use a "third order Newton's Divided Difference Polynomial" to interpolate the results between different grids. However, I have not seen the use of higher order interpolation methods elsewhere than in this paper. I would appreciate any recommendations on literature regarding methods for interpolation. [1] Celik, I., Karatekin, O. Numerical experiments on application of Richardson extrapolation with nonuniform grids (1997) Journal of Fluids Engineering, Transactions of the ASME, 119 (3), pp. 584-589.

February 17, 2011, 11:07	Update#2	#3
gravis Member Reine Granström Join Date: Apr 2009 Location: Sweden Posts: 43 Rep Power: 17	Also, correct me if I am wrong, as I have understood a 1D linear interpolation (CDS) between two nodes of a regular grid is second order accurate. i.e. the leading truncation error term is proportional to the square of the distance between the nodes and the polynomial order is 1. And, as I have understood, a trilinear interpolation is identical to three successive linear interpolations. Therefore, it seems to me that a trilinear interpolation (on a regular grid) should also be second order accurate. However, at Wikipedia's page for Trilinear_interpolation it is written that: "The order of accuracy is 1 for all these interpolation schemes" (linear, bilinear and trilinear ) Can someone clear this out for me? Is it a general statement that holds for all grid types?

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February 18, 2011, 07:01		#6
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,870 Rep Power: 144	I think you would have to talk to CFX support for the details of the interpolators, beyond what is shown in the documentation.