I'm trying to plot streamlines of Stokes solution to an sphere, the expression of streamlines is
I've seen similar questions before and this what I have tried
As you can see, a=1, U=1, but it seems not to work, any help? Thanks
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1$\begingroup$ Never post unsearchable pictures of equations. Instead typeset them, using MathJax or at lest copyable code. $\endgroup$– David G. StorkJun 24, 2020 at 20:51
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2 Answers
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Perhaps ContourPlot is what you are looking for?
Try (Thanks to
MarcoB for his answer and definition of simpler)
ContourPlot[simpler, {x, -2, 2}, {y, 0, 2} ,Contours -> Table[-10^-i, {i, 0, 4}],MaxRecursion -> 4]
answered Jun 25, 2020 at 6:39
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$\begingroup$ That's what I need! Is there any way I can erase the streamlines inside the semicircle? $\endgroup$ Jun 25, 2020 at 19:22
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$\begingroup$ Add a constraint 'x^2+y^2>1 ' inside Contourplot. $\endgroup$ Jun 25, 2020 at 21:07
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$\begingroup$ for example
ContourPlot[…,RegionFunction->Function[{x,y},x^2+y^2>= 1]$\endgroup$ Jun 26, 2020 at 8:06 -
$\begingroup$ Oh yeah I was able to do that, I searched for it! Thanks I chose this as the answer, yet MarcoB's answer really did help. $\endgroup$ Jun 26, 2020 at 15:01
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expr =
With[
{r = Sqrt[x^2 + y^2], theta = ArcTan[x, y]},
-1/4 (Sin[theta]^2) (1/r - 3 r + 2 r^2)
]
simpler = FullSimplify[ExpandAll@expr]
Region[
ImplicitRegion[simpler == 0, {{x, -2, 2}, {y, 0, 2}}],
Axes -> False, Frame -> True,
PlotRange -> {{-2, 2}, {-2, 2}}
]
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$\begingroup$ It does work, but what when I try a value of psi other than zero it says Region Embedding dimension:2. I'm new to mathematica so I really don't know what it means. $\endgroup$ Jun 24, 2020 at 22:20