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Ellipse shape using flc2hs function

Posted Jul 26, 2022, 10:09 a.m. EDT Geometry, Modeling Workflow Version 6.0 3 Replies

dylan le maux
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Hello,

I'm working on a 3D model with the level set method and I would like to create an entry with an ellipse shape using the flc2hs function but I'm struggling on how to set the parameters of this function.

The equation of the ellipse is (x-x0)²/a²+(y-y0)²/b² = 1, with (x0 y0) as the center of the ellipse and a and b the radiuses of the ellipse. How can I implement this in the flc2hs function ?

Thanks !

3 Replies Last Post Aug 23, 2022, 9:56 a.m. EDT
Jeff Hiller COMSOL Employee

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Posted: 2 years ago Jul 26, 2022, 12:15 p.m. EDT
Updated: 2 years ago Jul 26, 2022, 1:59 p.m. EDT

Hello Dylan,

You can find the exact mathematical definition of the flc2hs function in the Reference Manual for COMSOL Multiphysics version 6.0 on page 357. The idea is that it's a smoothed Heaviside function, with the width of the smoothed region controled by the second argument. Away from that smoothing region, it returns 0 if the first argument is negative, and 1 if it is positive.

In the attached toy model, I use flc2hs to define an inhomogeneous thermal conductivity such that there is an ellipsoidal zone with a low conductivity in the center of the domain and a high conductivity elsewhere, with a smooth transition between the two. After computing the solution, you'll see how that causes the heat flux lines to curve outward to "avoid" the low conductivity chunk, as expected.

Hope this helps.

Best,

Jeff

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Jeff Hiller
Hello Dylan, You can find the exact mathematical definition of the flc2hs function in the Reference Manual for COMSOL Multiphysics version 6.0 on page 357. The idea is that it's a smoothed Heaviside function, with the width of the smoothed region controled by the second argument. Away from that smoothing region, it returns 0 if the first argument is negative, and 1 if it is positive. In the attached toy model, I use flc2hs to define an inhomogeneous thermal conductivity such that there is an ellipsoidal zone with a low conductivity in the center of the domain and a high conductivity elsewhere, with a smooth transition between the two. After computing the solution, you'll see how that causes the heat flux lines to curve outward to "avoid" the low conductivity chunk, as expected. Hope this helps. Best, Jeff

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Dylan Le Maux
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Posted: 2 years ago Aug 23, 2022, 6:01 a.m. EDT

Thank you Jeff, it seems to work very well with the help of your model.

Thank you Jeff, it seems to work very well with the help of your model.
Jeff Hiller COMSOL Employee

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Posted: 2 years ago Aug 23, 2022, 9:56 a.m. EDT

Glad I could help!

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Jeff Hiller
Glad I could help!

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