Theory Manual Version 3.4
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Subsection 7.8.2: Gap Functions Up Section 7.8: Tied Fluid Interface Subsection 7.8.4: Discretization

### 7.8.3 Penalty Method

Let the tied interface viscous traction be described by the penalty function, where is a penalty factor associated with . The penalty factor is expressed in units of viscosity per length. Therefore, in an auto-penalty scheme, it may be scaled to the ratio of fluid viscosity to element thickness. Similarly, let where is a penalty factor associated with . Note that has units of length per viscosity. It follows that Given these relations, it can be shown that the directional derivatives of the various terms appearing in the integrand of are where .
Subsection 7.8.2: Gap Functions Up Section 7.8: Tied Fluid Interface Subsection 7.8.4: Discretization