Timeline for Why lattice Boltzmann despite its huge number of mesh points still has worse accuracy in comparison to FEM for calculating wall shear stress?
Current License: CC BY-SA 4.0
6 events
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| Aug 17, 2020 at 15:55 | comment | added | Mithridates the Great | It means lattice sites at 0$^{\circ}$, 90$^{\circ}$, 180$^{\circ}$ and 270$^{\circ}$ are halfways from the actual cylindrical boundary. In other directions, there might be a deviation from halfway. Overall, it means if you revolve your 2D axisymmetric geometry you would get a pipe that is different from my 3D voxelized model and that's the reason why you actually working on a cylindrical coordinate but my model works on a cartesian coordinate. In another word, you exploit symmetry of cylinder but my LBM framework because is written generally for unstructured models doesn't care about symmetry. | |
| Aug 17, 2020 at 15:53 | comment | added | Mithridates the Great | If you read the question carefully, you would find that I used BFL for boundary condition primarily, although I reported the halfway bounce back result as well. My point is that: Your model is 2D. When you use a 2D model to solve a 3D model like this in a pipe, you assume that everything is axisymmetric. But, in my implementation, my code only takes 3D models and it doesn't care about any symmetry in the geometry and generally use a graph-based unstructured model to voxelize any 3D geometry into cartesian voxels... | |
| Aug 17, 2020 at 7:01 | comment | added | nluigi | @AloneProgrammer should i assume that in your simple bounce back implementation you dont have the boundaries halfway between nodes? In that case you would have Full bounce back which is known to be first-order accurate and may explain the deviations for that implementation. | |
| Aug 17, 2020 at 6:56 | comment | added | nluigi | @AloneProgrammer i don't follow your point; 1. It is not really a hidden assumption as i mention halfway BB, 2. I dont see how the boundary location has to do with the coordinate system rather it is a result of the BC implementation, 3. How can a 2D axisymmetric cartesian framework (which this is actually not as i dont use symmetry) be identical to a 3D cylindrical coordinate framework? It would be missing terms related to the curvature of the pipe | |
| Aug 16, 2020 at 23:10 | comment | added | Mithridates the Great | It doesn’t surprise me that you saw a second-order convergence here cause there is a big hidden assumption here and that is: you assumed all the boundary nodes are halfway from actual cylindrical boundary and by axis symmetry it means your 2D cartesian axisymmetrical framework is identical to a 3D cylindrical coordinate. So it makes sense that you achieved this level of accuracy even with relatively coarse lattice size. If you try to implement a full 3D framework instead of using 2D axisymmetrical model and approximate the cylinder by cartesian voxels, you would see similar worst accuracy. | |
| Aug 16, 2020 at 21:01 | history | answered | nluigi | CC BY-SA 4.0 |