Mesh size and accuracy of results

[tibich72]

Hope I've posted in the correct forum -- if not, please move to appropriate place.

I'm working on a simple problem which consists of a board, and component consuming power, all placed within an airbox. Elmer solves flow and heat equations. The ambient temperature (i.e. the temperature at the boundaries of the air box) is 25C. I'm using Gmsh to mesh the geometry, sometimes using the Netgen algorithm, and sometimes the Delaunay algorithm for obtaining the 3D elements (tetrahedras). In all experiments below, the .sif file was the same, only the mesh changed.

I'm far from being an expert in numerical methods and/or finite element methods, so maybe what I'm asking is obvious.

I've noticed that different mesh sizes gives me very different results. I'm listing some of the results here (showing the mesh size, max temperature, and min temperature):

Code: Select all

10k  72C  23C
 20k  63C  20C
 23K  65C  20C
 24k  61C  23C
 71K  78C  22C
102K 80C  16C

There does not seem to be any correlation between the mesh size and the min/max temperatures; furthermore, the variation of results is very large: about 25% for max temperatures and about 30% for min temperatures. Does this mean that somehow the model is incorrect? Or is this something that should be expected when solving numerical problems with finite element methods? Can the results be so highly dependent even on the algorithm used for meshing? (For example, the 23K result was with Delaunay, the 24K result was with Netgen; both were optimized after meshing and, according to Gmsh, the overall quality of the mesh as well as the quality of extreme elements was about equal).

I'm wondering what's the way to get some stable results? Do I have to go to an extremely fine mesh (>300k? >500k? elements), or do I have to run dozens of experiments and get an average?

Any suggestion/answer/advice for good practice is highly appreciated. Thank you.

[gsal]

Hhhmmm, I am not an expert, either, but since nobody else seems to be giving any feedback, I will take a shot at it.

Yes, making the mesh finer and finer will tend towards the correct answer. When you are doing something for the first time and have no experience on mesh size, I would opt for experimenting with it and see if the results tend to move close and closer towards a visible asymptote. To start with, you should probably model something for which you already know the solution or can easily get it some other way...simple enough model for a hand calculation or matlab or something, or complex just enough for the solution to depend on mesh size.

I am yet to experiment much for Elmer, but I do know that in other FEA solvers, the application of the forces or boundary conditions or whatever, can be done in more than one way...some times it is based upon the total area regardless of the number of nodes you end up with after meshing, but sometimes it is on a per node basis...if you are applying your force on a per node basis, then, the more nodes you have the more force you are actually applying and do not realize....do a summation of certain quantities in your model and double check that what you think you are applying is in fact all there is in the model and not more.

Anyway, just use common sense and query your model ( I know, common sense is the least common!)

my 2 cents.

good luck

gsal