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

uniform spacing mesh and no-uniform mesh

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

Like Tree8Likes
  • 2 Post By PenPencil
  • 2 Post By FMDenaro
  • 2 Post By naffrancois
  • 2 Post By andy_

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   May 9, 2021, 07:52
Default uniform spacing mesh and no-uniform mesh
  #1
Member
 
Mercurial
Join Date: Mar 2021
Posts: 66
Rep Power: 3
Techies is on a distinguished road
Hi all,
I read the document about the cfd, they said that the uniform spacing mesh has rectangular mesh with second order accuracy and the nonuniform mesh (the changes of mesh take place within domain)is only of first order accuracy
So the uniform mesh is better than non uniform mesh ? Is this true ?
Techies is offline   Reply With Quote

Old   May 10, 2021, 08:08
Default
  #2
New Member
 
Icaro Amorim de Carvalho
Join Date: Dec 2020
Posts: 23
Rep Power: 3
PenPencil is on a distinguished road
No. This is a much more complex matter. Second-order accuracy can be obtained with nonuniform meshes, thank goodness. Otherwise we would have a very big problem to refine any domain from the wall outwards.
naffrancois and Techies like this.
PenPencil is offline   Reply With Quote

Old   May 10, 2021, 12:05
Default
  #3
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,099
Rep Power: 66
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
The type of computational mesh has nothing to do with the order of accuracy. You have to check the local truncation errro of the discretization to talk about accuracy.
On non-uniform grid you can get any accuracy order, provided that the scheme is suitably built.
naffrancois and Techies like this.
FMDenaro is offline   Reply With Quote

Old   May 11, 2021, 04:18
Default
  #4
Senior Member
 
Join Date: Oct 2011
Posts: 168
Rep Power: 12
naffrancois is on a distinguished road
As suggested by FMDenaro this topic is strongly related to the truncation error of the spatial scheme.

For a given grid nodes number and a consistent scheme (at least 1st order), uniform spacing will not give you the lowest global error.

The reason is that minimum overall error is reached when truncation error is minimized. Truncation error is however never constant over the domain as it depends also on higher derivatives of the solution. In an attempt to equi-distribute/minimize truncation error grid points have to be moved.
FMDenaro and Techies like this.
naffrancois is offline   Reply With Quote

Old   May 12, 2021, 04:46
Default
  #5
Senior Member
 
andy
Join Date: May 2009
Posts: 196
Rep Power: 15
andy_ is on a distinguished road
Quote:
Originally Posted by Techies View Post
So the uniform mesh is better than non uniform mesh ? Is this true ?
Quite often yes but as a general blanket statement no.

If what you are solving pushes the approach towards being close to uniform everywhere then a uniform grid with a high order numerical scheme is likely to be the most efficient approach. Acoustics and DNS/LES turbulence can be examples of this.

If what you are solving has a few strong local gradients with very much smaller ones throughout the rest of the flow then this pushes the approach towards a relatively low order scheme with strong variations in grid refinement. The low order scheme follows from high order schemes generally misbehaving badly when resolution is insufficient to resolve the gradients in the solution. Shock waves and free/boundary layers using RANS turbulence models can be examples of this.

As a final point. The order of the numerical scheme matters most when trying to drive the truncation error to negligible levels rather than living with a significant level and seeking to make the form more interpretable and/or better behaved physically (e.g. numerical diffusion). Consider a grid refinement study (e.g. sequence of grids halving the grid spacing everywhere) for a numerical scheme that is formally second-order accurate on a uniform grid and formally first-order accurate on a non-uniform grid. If the non-uniform grid is varied smoothly and well matched to the unresolved gradient (e.g. boundary layer) then the observed convergence rate over the range down to practical grid independence may be more like 1.9 rather than 1.0 with the uniform grid being 2. With the global error for the non-uniform grid on the coarsest grid level starting well below that of the uniform grid due to it's smaller grid spacing next to the wall the non-uniform grid may well reach practical grid independence first (e.g. less than 1% error in relevant physical quantity). Of course if grid refinement is continued down towards round-off at some point the uniform grid will begin to have the lower global error but this is often largely irrelevant in real world simulations.
PenPencil and Techies like this.
andy_ is offline   Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
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 Off
Pingbacks are On
Refbacks are On



All times are GMT -4. The time now is 03:29.