Theory Manual Version 3.4
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Subsection 3.5.4: Special Boundary Conditions Up Subsection 3.5.4: Special Boundary Conditions Subsubsection 3.5.4.2: Tangential Flow Stabilization

#### 3.5.4.1 Backflow Stabilization

For arterial blood flow, backflow stabilization has been proposed previously to deal with truncated domains where the entire artery is not modeled explicitly [17, 31]; for these types of problems, letting or prescribing a constant pressure at the outflow boundary may not prevent flow reversals that compromise convergence of an analysis. Instead, these authors proposed a velocity-dependent traction boundary condition, with a tensile normal component, that counters the backflow (only when ). Here, is a non-dimensional user-defined parameter; a value of turns off this feature, while a value of generally shows good numerical performance. We adapt this previously proposed formulation by letting the normal component of the viscous traction be given by The choice of in lieu of is for convenience, to avoid the dependence of on (which is negligible for nearly incompressible flow). Then, the contribution of this traction to the virtual external work is The linearization of along an increment in the velocity is given by where The discretized form of is whereas the discretized form of is
A (viscous) tangential traction is implemented as a separate flow stabilization method in the next section, applicable to inlet or outlet surfaces, without a conditional requirement based on the sign of .
Subsection 3.5.4: Special Boundary Conditions Up Subsection 3.5.4: Special Boundary Conditions Subsubsection 3.5.4.2: Tangential Flow Stabilization