Timeline for Total flux of the gradient of the numerical solution of a PDE through a surface
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| Jun 23, 2021 at 13:23 | comment | added | umby | @Tim Laska, it works fine now, many thanks! | |
| Jun 16, 2021 at 20:46 | history | edited | Tim Laska | CC BY-SA 4.0 |
Updated the post to eliminate a warning on posXids = Position[center3[[All, 1]], _?(# >= 0 &), 1] // Flatten;
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| Jun 16, 2021 at 20:44 | comment | added | Tim Laska | @umby It gives a warning that you can ignore. I have updated the post with an expression that avoids the warning. | |
| Jun 16, 2021 at 8:54 | comment | added | umby |
However, this line posXids = Position[center3, _?(#[[1]] >= 0 &), 1] // Flatten gives an error message: Part::partd: Part specification List[[1]] is longer than depth of object. Can you please help me on this point?
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| Jun 16, 2021 at 2:19 | comment | added | Tim Laska |
@umby You will need to make a couple of changes tip=BoundaryDiscretizeRegion[Ellipsoid[{0, 0, 0}, {1, 1, p}], MaxCellMeasure -> .005, Axes -> True, AxesLabel -> {"X", "Y", "Z"}]; domCuboid=BoundaryDiscretizeRegion[ Cuboid[{-2.5, 0, -3.8}, {7.5, 4, 0}], Axes -> True, AxesLabel -> {"X", "Y", "Z"}]; and it will work. You need to coarsen the mesh on the tip otherwise gradT throws some errors presumably due to mesh quality. The second change is to make the ceilings of the domCuboid and refCuboid align.
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| Jun 15, 2021 at 15:00 | history | edited | Tim Laska | CC BY-SA 4.0 |
Fixed a typo in the code.
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| Jun 15, 2021 at 13:18 | comment | added | umby |
@Tim Laska, your code can be applied to different geometries, as an ellipsoid with two axes of length 1 and a third axis of length p? In this case the geometry description would be: p=2; Pe=15; tip=BoundaryDiscretizeRegion[Ellipsoid[{0,0,0},{1,1,p}],MaxCellMeasure->.00125,Axes->True,AxesLabel->{"X","Y","Z"}]; refCuboid=BoundaryDiscretizeRegion[Cuboid[{-1.5,0,-p-0.5},{3.5,1.5,0}],MaxCellMeasure->.01,Axes->True,AxesLabel->{"X","Y","Z"}]; Your section "Summing up the discretized data", seems suitable for any geometry, or does it need an adjustment?
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| Jun 4, 2021 at 1:03 | history | edited | Tim Laska | CC BY-SA 4.0 |
Added a parametric sweep of Péclet numbers.
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| Jun 3, 2021 at 14:33 | comment | added | Tim Laska | @umby See update. | |
| Jun 3, 2021 at 14:32 | history | edited | Tim Laska | CC BY-SA 4.0 |
Updated in response to @umby's comment
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| Jun 3, 2021 at 9:52 | comment | added | umby | @Tim Laska, I have to confess I did not really catch the core of your solution, and this is my fault alone. For example, I do not understand why your solution does not work for small value of Pe (Pe is the Peclet number, so a small Pe means a slow flow along X); the calculated temperature field is quite unrealistic in this case. But it seems to me that your code contains only a splitting of the domain and a mesh refinement function. Or probably this arises from the asymmetric nature of the domain with the upstream section much shorter than the downstream region? | |
| Jun 1, 2021 at 3:29 | comment | added | Tim Laska | @umby Thank you very much! I will see what I can do. | |
| May 31, 2021 at 14:26 | vote | accept | umby | ||
| May 31, 2021 at 14:26 | comment | added | umby | @Tim Laska, this is more than I expected!! I am more than grateful. To justify my silence: I am studying your code and I will surely ask you some questions soon (if I can bother you again). | |
| May 31, 2021 at 11:25 | comment | added | ABCDEMMM | thanks for your reply! Actually, I am looking for an example for Staggered Scheme for NDsolve coupled fields. or in other words, how to set the staggered solver in mathematica. | |
| May 31, 2021 at 2:08 | comment | added | Tim Laska | @ABCDEMMM Of course, the subject of FSI is very broad and generally quite difficult. If you can assume that the deformations are so small that they do not affect the fluid flow (e.g., thermal stress due to transient transfer from a fluid), then you could do a "FSI" problem following this example. Significant deformation would require the ability for Mathematica to solve the mesh deformation equations on the fluid side, which I have yet to see an example. Consider making a feature request. | |
| May 30, 2021 at 23:09 | comment | added | ABCDEMMM | Is it possible that we can solve coupeld pde (e.g. FSI) using Mathametica Solver? | |
| May 30, 2021 at 19:06 | history | edited | Tim Laska | CC BY-SA 4.0 |
Added a comparison comparison of Mathematica results to COMSOL and minor grammatical corrections.
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| May 29, 2021 at 18:00 | history | edited | Tim Laska | CC BY-SA 4.0 |
Added a section to estimate total flux.
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| May 29, 2021 at 4:38 | history | answered | Tim Laska | CC BY-SA 4.0 |