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Normal and Tangential derivatives at boundary

Posted 2020年12月4日 GMT-5 14:58 General, Geometry, Equation-Based Modeling 1 Reply

Avishai Benyamini
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Hi all,

I am solving a PDE with the Weak Form PDE in 2D. I have weak contributions defined on the boundary that need to be defined with respect to derivatives normal and tangential to the boundary. How do I write those derivatives?

For example I have a boundary along the y-axis with a weak contribution of, say, uytest(u) or uxtest(u). The normal direction here \hat{n}=\hat{x} and the tangential direction is \hat{t}=\hat{y}.

What will be the right way to write 'un' or 'ut' derivatives for an arbitrary geometry?

Thanks a lot, Avishai

1 Reply Last Post 2020年12月4日 GMT-5 16:05
Avishai Benyamini
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Posted: 4 years ago 2020年12月4日 GMT-5 16:05

I think I solved this.

In 2D (nx,ny) will be the normal units vector, and using a convention of \hat{n}\times\hat{t}=+\hat{z}, I can define a tangential unit vector by (-ny,nx).

I think I solved this. In 2D (nx,ny) will be the normal units vector, and using a convention of \hat{n}\times\hat{t}=+\hat{z}, I can define a tangential unit vector by (-ny,nx).

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