CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Points Per Wavelength

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   October 6, 2014, 11:48
Default Points Per Wavelength
  #1
New Member
 
Issac Mamed
Join Date: Oct 2014
Posts: 1
Rep Power: 0
issacmamed is on a distinguished road
Hi,
I am trying to find the grid points per wavelength PPW requirement to achieve a phase speed error less than 0.1 percent for sixth order non compact and compact centered approximations to a first derivative.

I looked everywhere but cannot find the relationship between PPW and phase speed error and also how it relates to the Taylor Series expansions in the non compact and compact schemes.

Please help me out.
Thx
Issac
issacmamed is offline   Reply With Quote

Old   October 6, 2014, 17:16
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,693
Rep Power: 33
FMDenaro will become famous soon enoughFMDenaro will become famous soon enough
Quote:
Originally Posted by issacmamed View Post
Hi,
I am trying to find the grid points per wavelength PPW requirement to achieve a phase speed error less than 0.1 percent for sixth order non compact and compact centered approximations to a first derivative.

I looked everywhere but cannot find the relationship between PPW and phase speed error and also how it relates to the Taylor Series expansions in the non compact and compact schemes.

Please help me out.
Thx
Issac
I don't know if I got your question ... you want to get a formula to be compared to the exact first derivative of a function f(x) = f(k) exp(ikx).
Therefore you have the exact derivative

f'(x) = ik f(x)

and, on the other hand, a generic discrete operator Dn for the derivative will give you

Dn f(x) = ik_eff f(x)

being k_eff the resulting (can be also a complex number) modified wavenumber.
In conclusion, the local truncation error can be written as

L(x) = (d/dx - Dn) f(x) = i (k-k_eff) f(x)

and you want to minimize k-k_eff.

I suppose that one can start from the Nyquist theorem that says the minimum waveleght described on a grid needs at least of three grid points.
So you can start checking the error for several choices (that is for several k_eff)...
FMDenaro is offline   Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
.STL: non-closed manifold surface giulio.topazio OpenFOAM Native Meshers: snappyHexMesh and Others 32 November 25, 2016 04:15
No layers in a small gap bobburnquist OpenFOAM Native Meshers: snappyHexMesh and Others 6 August 26, 2015 09:38
determining displacement for added points CFDnewbie147 OpenFOAM Native Meshers: snappyHexMesh and Others 1 October 22, 2013 09:53
[DesignModeler] DM's JScript: FPoint()'s GetPoint(i) function picks points backwards? ANT ANSYS Meshing & Geometry 2 July 23, 2012 15:25
BlockMeshmergePatchPairs hjasak OpenFOAM Native Meshers: blockMesh 11 August 15, 2008 07:36


All times are GMT -4. The time now is 23:24.