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The UP algorithm
The method simply relies upon the observation that:
elem
ϕ p
The direction of the discrete
normal coincides with the
resultant of internal forces due
to an arbitrary but uniform
pressure (say, p=1) in the
whole fluid domain.
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ϕ = f ⎯⎯⎯⎯⎯→ n = ϕ / ϕ
elem elem Assembly
p
p p elem
ϕp=
∑ϕp
p p
elem
• Computationally inexpensive because f p are computed anyway.
• Ensures perfect equilibrium and therefore avoids shortcomings of
purely geometrical methods e.g. with warped 3-D faces.
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Shortcomings of the UP algorithm
• It fails at submerged
structural edges with no
topological thickness: the
assembled force vanishes
and thus the normal is
undetermined.
• It may yield at most
one normal per node.
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