[9mile]

Hi all.

I am studying a grid convergence test.

To compare the solution on fine and coarse mesh, following equation of L2 norm is used.

Norm = sqrt{sum over i~N of (u_i,c - u_i,f)^2/N},

in which u_i,c is a solution of coarse grid and u_i,f means a solution from fine mesh.

Sorry for crude expression of equation.

Anyway, total number of grid, N, is different on both meshes, then how can compare solutions one on one?

Any comments or guidance is appreciated
Thanks in advance.

[FMDenaro]

I attach some notes, sorry that are in italian but I hope the equations can be useful...

[9mile]

Thanks FMDenaro for your reply.

As i read your document, N of coarse grid is a reference value.

With doubling N, 2(N-1)+1 component is compared to one from N.

As for 4N, 4(N-1)+1 component could be compared to N.

Is it right ?

Regards

[FMDenaro]

Originally Posted by 9mile

Thanks FMDenaro for your reply.

As i read your document, N of coarse grid is a reference value.

With doubling N, 2(N-1)+1 component is compared to one from N.

As for 4N, 4(N-1)+1 component could be compared to N.

Is it right ?

Regards

Hello,

n is the number of component available on the coarsest grid therefore is also the number of values to extract from the vectors computed on the finer grids.

n_f is the number of points on the finest grid you can compute.

my example consider the fact the the points on the coarser grid has correspondence on the points on the finer (see figure).


You can find also some example in the book of Ferziger

[9mile]

Thanks FMDenaro.

It will be much help.

Kind regards.

[Tony12]

9mile,

Based on your ("crude") equation, it looks like the number of grid points, N, should be from the coarse mesh. The assumption here is that within your u_i,f vector, you only consider grid points that are in a similar location in x,y,z space as your fine grid (i.e. that you're comparing solution values that are in the same spatial position). So you'll have to write a script that can find all coarse mesh grid point locations and then find all fine mesh grid locations that match up (or interpolate -- preferred method), and use only those fine mesh locations for your equation.

[Martin Hegedus]

If possible, the overlapping points should be compared.

Here is an example of a grid convergence study I did for my code using the Vassberg grids.

http://www.hegedusaero.com/examples/.../Vassberg.html

Good luck.

[9mile]

Thanks Tony & Martin.

Information above are definitely helpful to me.

Regards.