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We present a numerical method to model the dynamics of inextensiblebiomembranes in a quasi-Newtonian incompressible flow, which better describeshemorheology in the small vasculature. We consider a level set model for thefluid-membrane coupling, while the local inextensibility condition is relaxedby introducing a penalty term. The penalty method is straightforward toimplement from any Navier-Stokes/level set solver and allows substantialcomputational savings over a mixed formulation. A standard Galerkin finiteelement framework is used with an arbitrarily high order polynomialapproximation for better accuracy in computing the bending force. The PDEsystem is solved using a partitioned strongly coupled scheme based onCrank-Nicolson time integration. Numerical experiments are provided to validateand assess the main features of the method.

A Finite Element Approach For Modeling Biomembranes In Incompressible Power-Law Flow