it's been a while since i have started a thread. i was wondering if we could discuss adaptive meshing. if anyone can give references to papers on adaptive meshing/automatic mesh refinement. also has anyone used the automatic meshing feature on commercial/public domain codes? if so which ones? and what's your take on their effectiveness? i think adaptive meshing is very important in the solution of multidimensional flows and hasn't been given due attention in journals. does anyone else have opinions? comments? let's start one of those nice in depth discussions.

Hi,

Adaptive meshing was my job for a some time and I think I've got opinions to offer. I did automatic error-driven mesh adaptation both in my own and in a commercial CFD code. At the time my main interest was a-posteriori error estimation and I think I have that one pretty much sorted out. As far as references go, I've got 4 papers under review (both on error estimation and mesh adaptivity), bu if people are interested I can provide copies.

The way I see mesh adaptivity is through modification of an existing mesh based on an a-posteriori error estimate, whith additional (discrete) description of the boundary if the coarse mesh does not describe it well. The algorithm I developed allows for embedded mesh refinement with directionality (the refined mesh orients itself to resolve the gradient) and arbitrary coarsening (there's no "refinement history" to replay backwards, you simply remove cells!). I used the 1-irregularity principle to control the mesh grading, as this is NOT guaranteed by error estimates. It's all nice an automatic, it works, there are solutions and I'm quite happy with the mechanics of the whole thing (solution mapping, dealing with mesh motion etc etc.).

HOWEVER (I think you saw this one coming from a mile away):

1) when you do supersonic flows with shocks, everything works like a fairy-tale. Shock resolution improves, cell count increase is moderate (in 3-D you only refine 2 2-D shock surface, which is nice!). The only thing you have to be careful about is not to formulate a stupid error indicator/estimate which gets bogged down on the strongest shock. Overall, life is good and easy. BTW, there's tons and tons of publications on this area...

2) laminar flows. Here, the problems start. Typically the solution is very smooth and the error comes from the mesh (non-orthogonality, sharp grading) and numerics (numerical diffusion) just as much as from poor mesh resolution. Now, here it is relatively easy to push the (estimated) discretisation error below 0.1% (maybe a couple of hundred thousand cells in 2-D). Suddenly, the adaptivity is very sensitive on mesh quality and it is necessary to do nice things to refined meshes - smoothing, orthogonality control and similar. Basically, if you want to get a real solution you heed to combine h- and r- refinement. Harder, but still manageable, mainly because errors are low to start with. When you plot the performance of the adaptive procedure against uniform refinement, two things happen: i) you are dissapointed; ii) you need to come up with some good excuses. Not so much published material here, a few lid-driven cavities (singular!) and not much else.

3) Turbulent flow. This gets really hard! As a reference I qouted only TWO papers where people tried to do adaptivity and turbulence (and I personally know both of them!). First, let's look at the flow: big gradients in velocity in boundary and shear layers. Second: mathematical model: k and epsilon are functions of (square of) velocity gradients and they get even sharper! (I quote k-e as the "standard treatment of turbulence today). Even worse trouble comes from the near wall treatment:

a) wall functions. This is a badly behaved 1-d model coupled to your 3-D N-S simulation and it causes mess because it limits refinement near the wall in terms of modelling error. And guess where the error is (no prizes): near the wall! So, after a few levels of refinement, the peak error hides next to the wall and you can't touch it. I also found that some non-linear k-e models (Shih etal) are singular with wall functions and mesh refinement at the reattachment point: without violating y+ epsilon increases without bounds!

b) low-Re. Now, this is a waell behaved model, meaning that the solution does not depend on the near-wall resolution (if you've got enough!). But now I have to resolve the gradients near the wall, which, according to the error estimate (and common sense) are huge! I tried doing mesh adaptivity with low-Re (never published before!) on a 2-D flow over a hill and I ended up on 300000 CV before I blinked (and the error has only just started coming down). this is really heavy stuff and I need massive computers for it (even in 2-D).

How to save youself? Well, go into 3-D! There, the "normal" meshes are so bad that adaptivity does something to the solution before getting stuck on the wall function problem, so the results look better.

In conclusion, I would say that this is a promising but immature technology. I am doing something on this front and will probably push it for a few more years. I think the computers wil soon be able to deal with it, but there's LOTS of work to be done.

If anyone wants my papers on this (unfortunately still under review), send me an E-mail. The references are quoted below:

@Unpublished{Jasak:ERRORADAPTIVE, author = {Jasak, H. and Gosman, A.D.}, title = {Automatic resolution control for the Finite Volume

Method. Part 2: Adaptive mesh refinement}, note = {Submitted to Numerical Heat Transfer}, }

@Unpublished{Jasak:ERRORTHEORY, author = {Jasak, H. and Gosman, A.D.}, title = {Automatic resolution control for the Finite Volume

Method. Part 1: {\it A-posteriori} error estimates}, note = {Submitted to Numerical Heat Transfer}, }

@Unpublished{Jasak:RESIDUAL, author = {Jasak, H. and Gosman, A.D.}, title = {Residual error estimate for the Finite Volume

Method}, note = {Submitted to International Journal for Numerical Methods in Fluids} }

@Unpublished{Jasak:LOCALPROBLEM, author = {Jasak, H. and Gosman, A.D.}, title = {Local Problem Error Estimate in Finite Volume

Discretisation}, note = {Submitted to Computers and Fluids}, year = 1998, month = {May} }

(1). This is a rather advanced topics. And I don't know whether the vendors of mesh generation codes like to hear it or not. I mean without the adaptive meshing, the world is black-and-white.(rather straightforward) (2). "the adaptive meshing" means that the mesh must be changed based on "the solution", using some kind of criteria. (3). This is not a new area of research, some works have been done back in 80's. (4). In the use of commercial codes, I have used the adaptive meshing options in Fluent/UNS and /Rampant codes for a couple of years. And I think, it is a nice feature of the codes. It was mainly used to refine the mesh locally, in order to see the solution more clearly. That is if you are serious about the accuracy of the solution, and also about the mesh independent solution, then the local mesh refinement is a good option. (5). Since the adaptive meshing in general codes has to be done interactively, the exact process depends mainly on the user's experience on the problem itself. (6). And each time one changes the mesh, it will take more time for the solution to converge. (7). I think, without the adapting meshing, the world is black-and-white. You simply refine the mesh and get another solution, and repeat the process until the final solution is mesh independent.(in any way you like) (8). With the adapting meshing, the criteria to change the mesh become new problems. And with the final solution unknown, it is somewhat difficult to know the right way to go.

gentlemen thanks for the response i hope that more forum users will contribute to this thread. let me give you more detail where i'm coming from. i think i first encountered the concept of adaptive meshing in the FEM field wrt structural and conduction simulations. in these areas the problems are mostly linear and when they are nonlinear (example temp dependent conductivity) they are not too nonlinear (if you can say that). anyhow the concept of an error estimate makes sense all the time in those cases and as a result FEM code writers could choose between h or p refinement as they pleased. in any case it matters little because the effect is basically the same (there are issues but somewhat minor). so nowadays you can find h and/or p adaptive schemes on many commercial solvers eg pro/mechanica (p scheme). funnily enough because it is often possible to make a good mesh for these types of problems a priori the utility of adaptive meshing is often lost on the users of these programs, also with some of these codes the user doesn't even know that the mesh is being adapted (especially where a p scheme is used because you don't see a change in the elements). at that time i wasn't paying much attention to CFD so i didn't know much about what was going on there, but since i've been in grad school i pay more attention know and i've seen more on the topic. (cont'd next post)

(continuing) i think the first time i'd seen anything on adaptive meshing was in John Anderson's CFD book although the concept looked kinda strange on structured grids. last year i saw two papers which used adaptive meshing. one was by a guy named Danenhoffer who works for Pratt & Whitney/UTRC (in a VKI lecture series book) and another by Bijan Mohammadi (it turns out he didn't do the refinement stuff just the CFD code) who works at INRIA (you can get his CFD and the adaptive mesh gen codes by following links at capella.colorado.edu). these examples were a revelation to me because the use of unstructured grids (quads and tetrahedra respectively) made the concept seem like the best thing since sliced bread. since then i've seen other examples like Marsha Berger's scheme on top of Randy Leveque's CLAWPACK (which gives you AMRCLAW) and the amrita package. most of these programs/applications use either cartesian or tetrahedral meshes but unfortunately many of the codes are for things like simulating star clusters etc. (follow some of the links on Randy Leveque's CLAWPACK page (http://www.amath.washington.edu/~rjl/clawpack.html). i've seen quite a few papers dealing with typical flows or aerodynamic interest (wings,turbomachinery etc) so i guess it's not just star clusters. anyhow i have some questions /concerns. although some of these are addressed in Dr. Jasak's post. (1)i've seen unsteady analyses done using AMR but how is the logic of process laid out so that too much time is not wasted on the refinement/derefinement process. (2) are purely p methods widely used and if so what is the success. i ask because most of the work i've seen is h and/or r. (3)i know john made comment on this wrt to Fluent. but would others like to comment on this and other commercial/public domain codes. i've checked out CFDRC for example and they seem to have the widest range of adaptive capability on the market (cartesian, tetrahedrons, quads etc most with adaptivity) i'd like for others to give comments on these or other codes.(4)Hrvoje made a comment about wall laws (turb modelling) and AMR. it seems to me that if you're using wall laws, multilayer turbulence models or algebraic turbulence models that you might have problems particularly because some wall laws (perversely) don't like extremely small grids near the wall. i had a presentation in a turbulence class last week where a PhD student was talking about a wall law where if the first grid point was in the laminar sublayer then it didn't work even though his wall function was one of those 'universal wall functions'. seems fishy huh?(5) also we could talk about error estimates and other way to control AMR. actually i just want a nice long thread where we can discuss and disseminate some ideas.

Part I

I have seen a couple of presentations on this subject but I have to admit, cannot remember all the details. I think the code used was called COBRA and that it was applied to premixed combustion of methane -air. as well as traditional shocks over cylinders. I am sure that there was some 'galactic' modelling in there as well. I'll dig out the proceedings and, if it looks like it could add to this thread post something in 'Part II'!

Dear All,

Following a few E-mail requests, I have made pre-prints of my papers on error estimation and adaptive refinement in the FVM publicly available on the ftp site:

monet.me.ic.ac.uk

cd outgoing

The papers, with titles, abstracts etc will be incorporated into the Imperial College web site (monet.me.ic.ac.uk) within the next few days.

Regards,

Hrv

[santhip]

Hi ,

I am working in the area of Mesh Adaptation for my master's thesis. Right now I am working on a r-refinement Mesh Adaptation technique with truncation error of the numerical scheme throughout the domain as the adaption criteria, for the problem of Quasi-1D Nozzle. Truncation Error acts as source of Discretization Error for a numerical scheme, and also transports it. And the results for mesh adaptation based on this criterion looks promising, in terms of reduced Discretization Error, while solving 1-D Burger's Equation, for which Research has been carried out ( Reference: Strategies for Mesh Adaptation in CFD by Dr. Christopher Roy , AIAA 2009 Conference in Florida). Discretization Error based Mesh adaptation isn't better than Truncation Error as a mesh Adaptation Criterion for the Case involving Shock. See the paper for more details. Methods to Estimate truncation Error by using curve fits is also under research.

Other references I would recommend for Mesh Adaptation would be the papers by following authors in AIAA journals/conferences:
Baker ( Gives an overview about Different techniques used for Mesh adaptation )
Scott McRae ( Presents a good review about different Techniques )
Christopher Roy ( Truncation error based Mesh Adaptation )

I look forward to Discussion related to this topic in this thread.

Thanks,

Santhip

[sekkizhar]

check out 2005-01-02-07 SAE paper

[zhvickie]

An object-oriented and quadrilateral-mesh based solution adaptive algorithm for compressible multi-fluid flows, JCP, Volume 227 , Issue 14 (July 2008)

Originally Posted by clifford bradford
;7560

it's been a while since i have started a thread. i was wondering if we could discuss adaptive meshing. if anyone can give references to papers on adaptive meshing/automatic mesh refinement. also has anyone used the automatic meshing feature on commercial/public domain codes? if so which ones? and what's your take on their effectiveness? i think adaptive meshing is very important in the solution of multidimensional flows and hasn't been given due attention in journals. does anyone else have opinions? comments? let's start one of those nice in depth discussions.

[Flowee]

Hey Folks!

I hope you can help me.
I'm writing an essay for my university about criteria for adaptive mesh refinement in CFD problems (mainly automotive exterieur aerodynamics, no supersonic simulations)
I need some criteria, which indicate, that a specific area of the mesh needs refinement (e.g. pressure or velocity gradients,...)

Could someone send me papers, which are dealing with this problem, or name me some authors, who have concerned with this problem?

Thanks!

[zhvickie]

An object-oriented and quadrilateral-mesh based solution adaptive algorithm for compressible multi-fluid flows, JCP, Volume 227 , Issue 14 (July 2008)

Originally Posted by Flowee

Hey Folks!

I hope you can help me.
I'm writing an essay for my university about criteria for adaptive mesh refinement in CFD problems (mainly automotive exterieur aerodynamics, no supersonic simulations)
I need some criteria, which indicate, that a specific area of the mesh needs refinement (e.g. pressure or velocity gradients,...)

Could someone send me papers, which are dealing with this problem, or name me some authors, who have concerned with this problem?

Thanks!

[ganesh]

Dear Sandip,

I have worked in the area of mesh adaptation based on truncation error and continue to work on it. The following papers might be of interest to you, in addition to the works of Prof McRae and Christopher Roy that you have mentioned.

Aftosmis and Berger AIAA-2002-0863.
Hay and Vissoneau Computers and Fluids 2007 Vol 36 (8)
Hay and Vissoneau IJCFD 2006 Vol. 20(7)
Ganesh, Nikhil Shende and Balakrishnan Computers and Fluids Vol 38 2009.

The references in the last paper could also be useful. And to the best of my knowledge, there is no good error estimator at shocks (See the last paper and works of Karni and Krividnova, spearate papers referenced in the last paper). I hope this helps.

Regards,

Ganesh

[CFD man]

Hi every body
I faced a problem in using adapting mesh in dynamic mesh, when I use adapting mesh, dynamic mesh does not work, actually FLUENT give this message:

Warning: layering cannot be applied on adapted zone 4.
Warning: layering cannot be applied on adapted zone 4.
Warning: layering cannot be applied on adapted zone 4.done

I will really appreciate your help.
All the best

[D.W.]

Originally Posted by CFD man

Hi every body
I faced a problem in using adapting mesh in dynamic mesh, when I use adapting mesh, dynamic mesh does not work, actually FLUENT give this message:

Warning: layering cannot be applied on adapted zone 4.
Warning: layering cannot be applied on adapted zone 4.
Warning: layering cannot be applied on adapted zone 4.done

I will really appreciate your help.
All the best

This warning occurs when Fluent tries to apply Dynamic Mesh (layering method) in a cell zone that has already had some Mesh Adaption.

There is a note about this in Fluent User's Guide
e.g. ANSYS Fluent User's Guide (2022R1), p. 1720, in the section "Applicability of the Dynamic Layering Method":
"Note that you cannot use the dynamic layering method in conjunction with adaption in almost all cases. For more information on the available adaption methods, see Hanging Node Adaption and Polyhedral Unstructured Mesh Adaption in the Theory Guide."