| Author | Message | |||
     Britta Hagmeyer (britta) Member Username: britta Post Number: 18 Registered: 11-2006 |
Hello everyone! I want to examine the RMS error as a function of mesh node count to obtain the dependency of the RMS error of the simulation on the mesh node count. In the attached code I've experimented with the mesh control parameters described in the manual. I was able to obtain a mesh with the minimum node count of 8669 nodes (NGRID=1, REGRID=OFF, ERRLIM=3e-3). By increasing the ERRLIM-factor or by increasing NGRID while keeping the same ERRLIM-factor, I was able to increase the number of mesh nodes in the simulation. Now, I want to decrease the node count below the current minimum value of 8669 nodes to 1000-6000 nodes and compare the simulation's RMS error to the RMS error obtained with higher node counts. Is this possible in FlexPDE, and if so, how can it be done? Thanks! Cheers, Britta
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 969 Registered: 06-2003 |
The minimum mesh size is controlled by the needs of the problem. You have a very small circle inside a large container. Resolving the shape of the circle requires a minimum of eight cells around the circumference, and the adjoining cells must be of similar size, growing in size in a controlled way as you move away from the circle. Furthermore, you have an abrupt cutoff of input velocity at the edge of the circle. You need some mesh cells in this area to resolve the shape. The finite element method tries to fit the solution with polynomial (quadratic) patches. If the cells are too large, the solution cannot be approximated by quadratics, and the fit will show extreme oscillations. While in finite difference approximations you may be able to enlarge the cell size and get an increasingly meaningless answer, in finite elements you will get chaos. You can work with a smaller mesh if you use a 2D cylindrical model. Or, you can replace the circle with a square, which requires fewer cells for shape resolution. This produces an extremely noisy representation of the velocity around the inlet. Our goal with FlexPDE has been to ensure an accurate solution to the problem as posed, refining the mesh until this can be achieved. With the size and speed of modern computers, we see no point in minimizing mesh size below the needs of resolving the solution. | |||
| Britta Hagmeyer (britta) Member Username: britta Post Number: 19 Registered: 11-2006 |
Hello Mr. Nelson! I've read through the section 'Interpreting FlexPDE Error Estimates', and I've got some questions: How can I verify the FlexPDE solution of my posed problem? i.e., how can I estimate the solution errors and their magnitude and find out where they come from (e.g. from computer roundoff)? Is the RMS error already averaged over the amount of cells in the FEmesh? (What is the range(u) in the RMS average of dU/range(U) over the cells?) What do the a posteriori error estimates RMS error , XError and TError tell me about the accuracy of my solution? What is the 'true' solution to the posed problem? What do you mean by 'The error estimate is a local measure of how much variation of the solution would produce the computed error in the cell integral.'? Thank you very much for your help! Cheers, Britta |
Sim code