Timeline for Infinite expresssion 1/0 encountered when use NDSolve for 3D axisymmetric Navier-Stokes (Euler) equations
Current License: CC BY-SA 4.0
17 events
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| Apr 10, 2023 at 6:33 | history | edited | mike | CC BY-SA 4.0 |
make the title a little bit more presise
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| Apr 6, 2023 at 4:14 | history | edited | user21 |
edited tags
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| Apr 5, 2023 at 12:03 | vote | accept | mike | ||
| Apr 5, 2023 at 11:32 | answer | added | Alex Trounev | timeline score: 3 | |
| Apr 5, 2023 at 9:01 | comment | added | mike | @AlexTrounev: Their adaptive mesh method looks too complicated to me. I hope to take short cut with NDSolve. :-) | |
| Apr 5, 2023 at 8:56 | comment | added | mike | @MichaelE2: I tried. It does not help. Thanks again! | |
| Apr 5, 2023 at 8:50 | history | edited | mike | CC BY-SA 4.0 |
deleted 6 characters in body
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| Apr 5, 2023 at 4:54 | comment | added | Alex Trounev | @mike In the paper sited Thomas used adaptive mesh method proposed in arxiv.org/pdf/2102.06663.pdf | |
| Apr 5, 2023 at 0:36 | comment | added | Michael E2 |
@mike, try changing {x, -1, 0, 1} to {x, -1, 1}.
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| Apr 4, 2023 at 21:07 | comment | added | mike | @MichaelE2 Thanks for the suggestion. For your option, the error message I got is "Because the coordinates were explicitly given for the direction of independent variable x, the values of options {MaxPoints, MinPoints, StartingPoints, MaxStepSize,MinStepSize,StartingStepSize} will be disregarded for this direction". | |
| Apr 4, 2023 at 21:03 | comment | added | mike | @AlexeiBoulbitch you are right. with version 13.2, it is running now. By the way, because $-1<=x<=1$, I need to replace $1/x$ with Sign[x]/Sqrt[x^2+eps]$ | |
| Apr 4, 2023 at 14:42 | comment | added | Michael E2 |
Using a spatial grid with an even number of points will avoid $x=0$ and perhaps have small error. Unfortunately, there is still the problem of finding initial conditions for all the variables (= functions & their derivatives). Perhaps you can do that by hand. (How to get an even number of points: Method -> {"MethodOfLines", "TemporalVariable" -> t, "SpatialDiscretization" -> {"TensorProductGrid", "MaxPoints" -> 50, "MinPoints" -> 50}})
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| Apr 4, 2023 at 13:53 | comment | added | Alexei Boulbitch | The latter message suggests that you use an older version of Mathematica, do you? | |
| Apr 4, 2023 at 13:02 | comment | added | mike | @AlexeiBoulbitch: Thanks for your help. I replaced 1/x by 1/Sqrt[x^2+eps] and got error message: "Unable to find initial conditions that satisfy the residual function within specified tolerances. Try giving initial conditions for both values and derivatives of the functions". After I specify the initial derivatives for all 3 dependent variables, I got error message :"Nonlinear coefficients are not supported in this version of NDSolve." | |
| Apr 4, 2023 at 12:44 | comment | added | Alexei Boulbitch |
Having got what you wrote about the functions that are even in x I would still recommend replacing the terms like (3*Derivative[0, 1, 0][f][t, x, z])/x with (3*Derivative[0, 1, 0][f][t, x, z])/Sqrt[x^2+eps] where eps=0.00001 or so. This alone does not solve your problem, since the warning: "Unable to find initial conditions that satisfy..." pops up.
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| Apr 4, 2023 at 12:18 | history | edited | mike | CC BY-SA 4.0 |
added mathematica code
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| Apr 4, 2023 at 6:08 | history | asked | mike | CC BY-SA 4.0 |