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Permanent FSI treatment (2)
• Upon discretization, contact pressure is replaced by interaction force r
• Interaction force
is the resultant of
the contact pressure
at each node of the
interface
• For the moment, assume nodal conformity at the F-S interface
• Velocity compatibility condition vFin = vSin
is of the form Cv = b
therefore one may use Lagrange multipliers to find r (see Part 1)
r
• However, the following apparently simple question arises:
How does one define
“the” normal to a
discrete F-S interface?
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The 2-D plane case
Pioneering work (1980s) by Donea, Giuliani, Halleux:
n 1
n
n 2
L 2
• Physical intuition: the
discrete normal is some
average of the adjacent
sides normals: n = ( n1+ n2)/
n1+
n2
y
x
L 1
• Works well only in 2D
plane cases, and for uniform
mesh: L1 = L2
• In more general cases, the mass balance is incorrect: some fluid is
“gained” or “lost” at the interface corners
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