Analysis and approximation of the Cross model for quasi-Newtonian flows with defective boundary conditions

• A defective boundary condition problem is approximated by an optimization approach.
• The control problem is analyzed for an existence result and the Lagrange multipliers.
• Numerical experiments verify robustness of the developed decoupling algorithm.

A numerical method for a generalized-Newtonian fluid with flow rate boundary conditions is considered. The defect boundary condition problem is formulated as a constrained optimal control problem, where a flow balance is forced on the inflow and outflow boundaries using a Neumann control. The control problem is analyzed for an existence result and the Lagrange multiplier rule. A decoupling solution algorithm is presented and numerical experiments are provided to validate robustness of the algorithm.