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perpendicular projection

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Old   February 15, 2012, 06:01
Default perpendicular projection
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Janez Turk
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I'm developing solver for vector field (denoted n) that has only direction. It's length is always a unit. Therefore I must perpendiculary project any forces that act on the vector field.

The source term is projected by multiplication with projection tensor (I-n*n):
(I-n*n)&(source term of force).

Laplacian term can maintain implicit nature because it can take volTensorField as argument:

I would like to have the advection term also projected, as this is crucial to the solution, and maintain implicit nature. What shoud I do with fvm:div(phi,n) term ?

The equation looks like this:

fvm::ddt(n) + fvm::div(phi,n) - fvm::laplacian((I-n*n),n) == (I-n*n)&(many source terms)

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perpendicular, projection, projection tensor

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