Theory Manual Version 3.4
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Subsection 7.8.1: Contact Integral Up Section 7.8: Tied Fluid Interface Subsection 7.8.3: Penalty Method

### 7.8.2 Gap Functions

The premise of a tied interface is that the parametric coordinates of coincident points and on and are both invariants (i.e., they are determined in the reference configuration and remain unchanged over time). The parametric coordinates of correspond to the integration points on , and those of are evaluated once by shooting a ray from the integration point on to intersect .
The vector gap function , representing the difference between tangential velocities across the interface, is defined by where the tangential velocity is evaluate from We may similarly define the scalar gap function , representing the difference between fluid pressures across the interface, where is the fluid bulk modulus.
Subsection 7.8.1: Contact Integral Up Section 7.8: Tied Fluid Interface Subsection 7.8.3: Penalty Method