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

Grid refinement or Higher order scheme

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

Like Tree3Likes
  • 1 Post By AeroSonic
  • 1 Post By FMDenaro
  • 1 Post By FMDenaro

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   December 13, 2021, 14:13
Unhappy Grid refinement or Higher order scheme
  #1
Member
 
AeroSonic's Avatar
 
Yusuf Elbadry
Join Date: Sep 2018
Posts: 65
Rep Power: 7
AeroSonic is on a distinguished road
Hello,
I hope you are all fine,

I am solving the heaving airfoil problem while using the Eulerian grid (Level Set Method). The 2D Incompressible N-S equations are solved using GLS FEM. I am simulating the flow at Re=800, Angle of Attack =20 Deg. I am using bilinear shape function for geometry and solution and I am using an explicit scheme.

I have a problem with the accuracy of the result, I am comparing my result (Cl, CD) with the literature and the error is not small, and I was thinking to use a second-order shape function for both the geometry and solution to get a better result and better shape for the airfoil instead of stairs.

Would this be better or should I use a more refined grid with a very small time step?
MohamedAdawy likes this.
AeroSonic is offline   Reply With Quote

Old   December 13, 2021, 15:49
Default
  #2
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AeroSonic View Post
Hello,
I hope you are all fine,

I am solving the heaving airfoil problem while using the Eulerian grid (Level Set Method). The 2D Incompressible N-S equations are solved using GLS FEM. I am simulating the flow at Re=800, Angle of Attack =20 Deg. I am using bilinear shape function for geometry and solution and I am using an explicit scheme.

I have a problem with the accuracy of the result, I am comparing my result (Cl, CD) with the literature and the error is not small, and I was thinking to use a second-order shape function for both the geometry and solution to get a better result and better shape for the airfoil instead of stairs.

Would this be better or should I use a more refined grid with a very small time step?



Before introducing a higher order scheme, you must verify that your code works well for via via refined grids. If your solution does not improve under grid refinement, your problem is not the low accuracy order but some different issues.
AeroSonic likes this.
FMDenaro is offline   Reply With Quote

Old   December 13, 2021, 16:04
Default
  #3
Member
 
AeroSonic's Avatar
 
Yusuf Elbadry
Join Date: Sep 2018
Posts: 65
Rep Power: 7
AeroSonic is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
Before introducing a higher order scheme, you must verify that your code works well for via via refined grids. If your solution does not improve under grid refinement, your problem is not the low accuracy order but some different issues.
If the solution accuracy got better while using a fine grid, would it be better to use a higher-order scheme to reduce the number of elements and get a better airfoil shape, or should I continue with the refined grid? I know that this question is related to the computation time but I would like to reduce the computation time as possible as I can, as I am doing these simulations on my personal computer.

Thank you for your reply.
AeroSonic is offline   Reply With Quote

Old   December 13, 2021, 16:19
Default
  #4
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AeroSonic View Post
If the solution accuracy got better while using a fine grid, would it be better to use a higher-order scheme to reduce the number of elements and get a better airfoil shape, or should I continue with the refined grid? I know that this question is related to the computation time but I would like to reduce the computation time as possible as I can, as I am doing these simulations on my personal computer.

Thank you for your reply.



For an arbitrary fixed grid of size h, you cannot be sure that the solution obtained with a second order scheme is better than a first order scheme. You need to have a sufficient grid resolution to get a real improving. That is a classical topic in CFD.
FMDenaro is offline   Reply With Quote

Old   December 13, 2021, 16:58
Default
  #5
Member
 
AeroSonic's Avatar
 
Yusuf Elbadry
Join Date: Sep 2018
Posts: 65
Rep Power: 7
AeroSonic is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
For an arbitrarily fixed grid of size h, you cannot be sure that the solution obtained with a second-order scheme is better than a first-order scheme. You need to have a sufficient grid resolution to get a real improving. That is a classical topic in CFD.
Yeah, I got that. I just thought that if I used a 2nd order shape function or higher, I can get a better shape of the airfoil while using a small number of elements and nodes compared to the case while using a bilinear shape function in which I have to use a very very fine grid near the airfoil.

For example, if I have an airfoil with a chord of 1 (nondimensional length), I will need elements with a side length (in y-dir) of 3e-3 or less to have a smooth airfoil shape, If the airfoil will move in the y-direction with an amplitude of 0.5c (from -0.5c to 0.5c), then I need at least 333 divisions in this direction, and let us say I will have one-third of this number in the x-direction, this may result in around 350,000 elements near the airfoil where it moves, not mentioning the rest of the domain. This may result in a grid of more than 600,000 elements.

That is why I thought of using high order shape function, to reduce the number of elements and nodes.

I really appreciate your help and guidance and thank you for your patience.
AeroSonic is offline   Reply With Quote

Old   December 14, 2021, 04:24
Default
  #6
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AeroSonic View Post
Yeah, I got that. I just thought that if I used a 2nd order shape function or higher, I can get a better shape of the airfoil while using a small number of elements and nodes compared to the case while using a bilinear shape function in which I have to use a very very fine grid near the airfoil.

For example, if I have an airfoil with a chord of 1 (nondimensional length), I will need elements with a side length (in y-dir) of 3e-3 or less to have a smooth airfoil shape, If the airfoil will move in the y-direction with an amplitude of 0.5c (from -0.5c to 0.5c), then I need at least 333 divisions in this direction, and let us say I will have one-third of this number in the x-direction, this may result in around 350,000 elements near the airfoil where it moves, not mentioning the rest of the domain. This may result in a grid of more than 600,000 elements.

That is why I thought of using high order shape function, to reduce the number of elements and nodes.

I really appreciate your help and guidance and thank you for your patience.



I don't understand, the shape functions defines a certain functional relation for the unknown variables, what do you mean now for the highlighted statement? The better description of the airfoil geometry is a different issue.
However, grid size and accuracy order defines different topics and different limits.The former fix the range of resolved wavenumber in the solution, the latter is the theoretical and asymptotical velocity rate of the error decreasing. You could have also a spectral accuracy but if you have fixed the grid size you cannot resolve nothing greater than the Nyquist frequency.
sbaffini likes this.
FMDenaro is offline   Reply With Quote

Old   December 14, 2021, 13:59
Default
  #7
Member
 
AeroSonic's Avatar
 
Yusuf Elbadry
Join Date: Sep 2018
Posts: 65
Rep Power: 7
AeroSonic is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
I don't understand, the shape functions defines a certain functional relation for the unknown variables, what do you mean now for the highlighted statement? The better description of the airfoil geometry is a different issue.
However, grid size and accuracy order defines different topics and different limits.The former fix the range of resolved wavenumber in the solution, the latter is the theoretical and asymptotical velocity rate of the error decreasing. You could have also a spectral accuracy but if you have fixed the grid size you cannot resolve nothing greater than the Nyquist frequency.
If I understand correctly, in the Finite Element Method, you have shape functions for each variable or known and you have a shape function for the geometry. For the geometric shape function, if it is a bilinear, it means you have a rectangular element with 4 nodes, if it is bi-quadratic, you can have 8 or 9 nodes per element, this means, if you used a bilinear shape function, you will connect every two nodes by a line, and if you used a bi-quadratic shape function, you will connect every two nodes by a quadratic curve, this will lead to a better representation to the body (if you are using a fixed grid and the body is moving and you are using an algorithm to define which point is inside or outside the body).

Please correct me if I am wrong or if there is something I am missing.
AeroSonic is offline   Reply With Quote

Old   December 14, 2021, 15:35
Default
  #8
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AeroSonic View Post
If I understand correctly, in the Finite Element Method, you have shape functions for each variable or known and you have a shape function for the geometry. For the geometric shape function, if it is a bilinear, it means you have a rectangular element with 4 nodes, if it is bi-quadratic, you can have 8 or 9 nodes per element, this means, if you used a bilinear shape function, you will connect every two nodes by a line, and if you used a bi-quadratic shape function, you will connect every two nodes by a quadratic curve, this will lead to a better representation to the body (if you are using a fixed grid and the body is moving and you are using an algorithm to define which point is inside or outside the body).

Please correct me if I am wrong or if there is something I am missing.



But this is a further topic. Think about a BEM formulation (panel method), you can describe the airfoilf by using straight segment or curved step. Then you prescribe a functional relation for the distribution of singularity.

In you case you want to use elements that are not linear triangles but curved triangles and then use high order shape functions.

Again, on the same and arbitrary mesh size h you cannot say a-priori that the error is for sure lesser for the quadratic shape function. You need to assess that by a grid refinement study. Only at a certain value h you get a monotonically expected rate for the error.
FMDenaro is offline   Reply With Quote

Old   December 15, 2021, 14:02
Default
  #9
Member
 
AeroSonic's Avatar
 
Yusuf Elbadry
Join Date: Sep 2018
Posts: 65
Rep Power: 7
AeroSonic is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
But this is a further topic. Think about a BEM formulation (panel method), you can describe the airfoilf by using straight segment or curved step. Then you prescribe a functional relation for the distribution of singularity.

In you case you want to use elements that are not linear triangles but curved triangles and then use high order shape functions.

Again, on the same and arbitrary mesh size h you cannot say a-priori that the error is for sure lesser for the quadratic shape function. You need to assess that by a grid refinement study. Only at a certain value h you get a monotonically expected rate for the error.
I am sorry, but I didn't understand the part related to the BEM and the panel method. I drew this comparison between a grid with bilinear and bi-quadratic shape function for the geometry, I meant that increasing the order of the geometrical shape function will allow me to get a better shape for the body.

I really appreciate your patience and your reply.
Attached Images
File Type: jpg Capture.jpg (48.2 KB, 6 views)
AeroSonic is offline   Reply With Quote

Old   December 15, 2021, 14:59
Default
  #10
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AeroSonic View Post
I am sorry, but I didn't understand the part related to the BEM and the panel method. I drew this comparison between a grid with bilinear and bi-quadratic shape function for the geometry, I meant that increasing the order of the geometrical shape function will allow me to get a better shape for the body.

I really appreciate your patience and your reply.
You are confusing the things in the problem. From your figure, the airfoil is still described by a step-by-step approximation. What you need is to adopt curved elements. On the other side, quadratic shape functions on linear-edge element can be effective in improving the fluid solution.
FMDenaro is offline   Reply With Quote

Old   December 16, 2021, 13:26
Default
  #11
Member
 
AeroSonic's Avatar
 
Yusuf Elbadry
Join Date: Sep 2018
Posts: 65
Rep Power: 7
AeroSonic is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
You are confusing the things in the problem. From your figure, the airfoil is still described by a step-by-step approximation. What you need is to adopt curved elements. On the other side, quadratic shape functions on linear-edge element can be effective in improving the fluid solution.
Yes, it is defined step by step exactly as in LBM for example.
I will try using a higher-order shape function for both and solution and geometry.
Thank you
AeroSonic is offline   Reply With Quote

Old   December 16, 2021, 13:33
Default
  #12
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AeroSonic View Post
Yes, it is defined step by step exactly as in LBM for example.
I will try using a higher-order shape function for both and solution and geometry.
Thank you

You could search for suitable isoparametric elements. On the other hand, the airfoil is better described by a triangular tesselation.
FMDenaro is offline   Reply With Quote

Old   December 16, 2021, 14:15
Default
  #13
Member
 
AeroSonic's Avatar
 
Yusuf Elbadry
Join Date: Sep 2018
Posts: 65
Rep Power: 7
AeroSonic is on a distinguished road
Quote:
Originally Posted by FMDenaro View Post
You could search for suitable isoparametric elements. On the other hand, the airfoil is better described by a triangular tesselation.
I know that there is a Lagrangian Element(9 nodes in case of bi-quadratic shape function) and Serendipity Element(8 nodes in case of bi-quadratic shape function), can I find a different element than these two types of the element?
AeroSonic is offline   Reply With Quote

Old   December 16, 2021, 14:25
Default
  #14
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,777
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by AeroSonic View Post
I know that there is a Lagrangian Element(9 nodes in case of bi-quadratic shape function) and Serendipity Element(8 nodes in case of bi-quadratic shape function), can I find a different element than these two types of the element?



Lagrangian simplex, that is triangular elements (or tetrahedron in 3D), having 3, 6, 10, ... nodes
FMDenaro is offline   Reply With Quote

Reply

Tags
fem, high order scheme., lsm

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


Similar Threads
Thread Thread Starter Forum Replies Last Post
Third order MUSCL Scheme 94bb494nd41f FLUENT 4 January 25, 2024 12:23
First Order to Higher Order Blending Factor NormalVector FLUENT 4 November 13, 2023 07:06
Implementation of higher order FD scheme near boundries pawank Main CFD Forum 16 September 23, 2016 08:52
Higher order downwind scheme jelmer OpenFOAM Running, Solving & CFD 4 August 9, 2006 06:43
Combustion Convergence problems Art Stretton Phoenics 5 April 2, 2002 05:59


All times are GMT -4. The time now is 08:44.