3d spline interpolation
Dear all,
I have to implement a soubroutine which interpolates the 3d velocity field {u, v, w} from a not equal spaced grid 1 to grid 2 where h is the grid size and h_1 smaller than h_2. In order to ensure a high order of accuracy I would like to use a spline interpolation. But I could not found the mathematics for the 3d approximation. Also google can not help me satisfactory. Has anybody the mathematics for me or can refer to a book. Thanks in advance. Matthias 
Re: 3d spline interpolation
Numerical Recipes is an online book with a reasonable chapter on interpolation and associated routines:
http://www.nr.com/ 
Re: 3d spline interpolation
If you have access to it, the NAG Fortran library may be of use.

Re: 3d spline interpolation
Dear Andy,
I have checked the Numerical Recipes online book, namely Chapter 3. It seems that it did not provide much useful information. For a 3d flow field interpolation as required when using Chimera grid, it will need a transformation of the cells to a rectangular one before the interpolation can be done. I also would like to have one such kind of subroutine as this kind of interpolation may be needed any time. It is certainly a waste of time if everyone has to implement such kind of subroutine on his own. Regards Li 
Re: 3d spline interpolation
My understanding of interpolation on overlapping grids (I have not done any myself) is that the form of the interpolation is very important in order to preserve conservation of integrated quantities between the two grids. I doubt that looking for general purpose interpolation routines is going to be a wise move.
To be a bit more constructive I am aware that Los Alamos did some work in this area in the late 80s/90s. They publicly released a fair amount of code and published a paper or two on the form of interpolation they used. Curiously the group seems to be at Livermore now: http://www.llnl.gov/CASC/Overture/he...ons/node2.html Unfortunately, the most relevant publication does not seem to be online. 
Re: 3d spline interpolation
Please use MATLAB tool to make 1D, 2D and 3D interpolation by spline or cubic. for 3D ==> interp3 Ok.

Re: 3d spline interpolation

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