Drag comparison upwind vs. scheme
Testing different computer configurations I noticed following problem.
Say that I simulate flow around the truck body on a given mesh. I start with the upwind differentation scheme having a drag of X. Afterwards I changed to hires and the drag reduces by approximately 25% and became not dependend on convergence level. I did not perform the mesh independence studies however I must say that the same situation occures in different simulaitons I perform of "abruptly" ended bodies, with sharp separation in the end of the body. For more "aerodynamical", "streamline" shaped bodies the difference between hires and upwind is much lower (for given mesh!!).
I would like to explain this. In generall the upwind and central schemes should give the same results on infinitely dense mesh. For finite density mesh there can be discrepancies but the higher order scheme should faster approach "real" solution on coarser mesh (am I right??).
- Does in mean, that in described case the drag predictions from hires scheme are closer to real ones? I mean, that if I dense the mesh the drag with upwind should be reduced?
- Does it mean that for "slim" bodies for given mesh, if the drag from upwing and hires is the same the solution is grid-independent???
I would be very grateful for help because it is related to rather big problems (many elements) and the calculation takes a lot of time, so it would be great to minimize number of grid/other studies.
In general, you are correct in saying that the higher-order scheme will approach the 'real' answer as grid definition increases. This is referred to as order of accuracy. However, this is independed from the actual magnitude of accuracy.
For low grid-resolutions, a lower order scheme can produce more accurate results. For example, if you double the grid density, then the first-order backwards scheme should give an improvement of 2¹ = 2, whereas the second order will result in 2² = 4. You can see that for high-accuracy calculations, you can easily reduce the number of gridpoints by using higher-order schemes.
thanks for Your answer, but can You clarify the statement:
For low grid-resolutions, a lower order scheme can produce more accurate results. For example, if you double the grid density, then the first-order backwards scheme should give an improvement of 2¹ = 2, whereas the second order will result in 2² = 4.
I did a mesh check, decreasing the size of elements in the wake by 3.
- in coarse mesh the drag force was 440N for upwind vs. 260N for hires
- in finer mesh the drag force was 340N for upwind vs. 250N for hires
Does in mean that hires shows "good" value on coarse mesh but performed coarening is still not enough for upwind?
Another aspect of this issue is that first order upwinding schemes have lots of numerical dissipation. This means they artificially increase the viscosity of the fluid. This increased viscosity means the simulation is running at a lower effective Reynolds number and therefore separation points will move, wakes will be different etc etc.
Your mesh sensitivity study is not surprising - the hires scheme is changing by 4% but the upwinding scheme is changing by 29%. This means hires is likely to be closer to mesh independance.
Have a look at Computational Fluid Dynamics by Roache for lots of detail on this area or http://journaltool.asme.org/Template...umAccuracy.pdf for how Journal of Fluids Engineering have taken as far as an editorial policy.
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