Discussion between Igor Kotelnikov and Alex Trounev

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14:22

Q: How do I pose Neumann boundary condition to suppress particles flux into zero point?

This is continuation from my previous post How to ensure for a solution of NDSolve to be positive? [https://mathematica.stackexchange.com/questions/278777/how-to-ensure-for-a-solution-of-ndsolve-to-be-positive] I'am trying to solve kinetic equation for the test particles injected into a Maxwellia...

Alex Trounev

Could you visualize solution without numerical artefacts by adding options PlotPoints -> 100 and Chop?

Igor Kotelnikov

@AlexTrounev. MWE updated as you have proposed.

Alex Trounev

Row 1 and 2 are very nice, but Row 3 pictures look wrong. Please, use option PlotPoints -> 100 without Chop for plt3DfluxLC and plt3Dflux.

Igor Kotelnikov

@AlexTrounev. I removed Chop@ but didn't notice any difference. Then I added "MaxRecursion->4" and again I didn't notice any change. The updated row 3 is now under the old row 3. Please note that radial flux oscillates around 0 near zero of velosity u.

Alex Trounev

Try

DensityPlot[    Norm[ flux[Sqrt[vx^2 + vy^2],              vx/Sqrt[vx^2 + vy^2], {\[Mu], \[Eta]}]] /. F -> fs, {vx,         umin, umax}, {vy, umin, umax}      , AxesLabel -> {"\!\(\*SubscriptBox[\(v\), \(z\)]\)",           "\!\(\*SubscriptBox[\(v\), \(\[UpTee]\)]\)"},    PlotLabel -> lbl,       PlotLegends -> Automatic      , ColorFunction -> Hue      , ImageSize -> iSize,       PlotRange -> Automatic, PlotPoints -> 100];

Igor Kotelnikov

14:22

@AlexTrounev: Done, Note that PlotRange was changed to Automatic.

Alex Trounev

Please, use exactly what I proposed {vx, umin, umax}, {vy, umin, umax}

Igor Kotelnikov

Okey, I added graphics both for small and lagre scales.

2 hours later…

Alex Trounev

16:23

Ok! Please, explain your problem with using pictures you uploaded.

5 hours later…

Igor Kotelnikov

20:56

I expect that radial flux near zero velocity u=umin tends to zero. From physics of the problem this would mean that the solution tends to Maxwellian distribution function. I expected that boundary condition NeumannValue[0, (0 <= \[Xi] <= 1) && (u == umin)] provides zeroing of the redial flux. But this is not the case.

Best of all it is seen from the right picture in the last row. This picture shows that solution is isotropic in the vicinity of u=umin as expected [we see no dependence on [Xi]]. However it shows thar radial flux does not tend to zero.

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