symmetric cubic spline

Lattice Boltzmann Method LBM: Theory
#1

Hi, guys

anyone can tell me what is symmetric cubic spline which is used in multi-block LBM?
where can I find reference about the kind of spline?

#2

hi

this is a good tutorial

http://www.physics.ge/books/1202559061Cubic%20Spline%20Tutorial.pdf

by the way I think you will get this equation


f(2.5) = 1/16 f(1) + 9/16 f(2) + 9/16 f(3)  1/16 f(4)

+-----+-----+-----+-----+-----+-----+
|     |     |     |     |     |     |      fine mesh
+-----+-----+-----+-----+-----+-----+
|     |     |     |     |     |     | 
f1----+-----f2---f2.5---f3----+-----f4
|           |           |           |
|           |           |           |      coarse mesh
+-----------+-----------+-----------+

regards

#3

Hi,SaS

It is very kind of you for giving me the material and the heuristic diagram.

In your opinion, the symmetric cubic spline is nothing but a special knots distribution. Do I understand your intention exactly?

#4

yes you can say that

but the exat definition is:


Cubic splines are a popular choice for curve fitting for ease of data interpolation, integration, differentiation,
and they are normally very smooth

The key characteristics of cubic spline interpolation are:
1. The curves pass through all specified data points
2. 1st derivative continuity at interior points
3. 2nd derivative continuity at interior points
4. boundary conditions specified at the free ends