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Aymen Laadhari; Ahmad Deeb

Computational Modeling of Individual Red Blood Cell Dynamics Using Flow Composition and Adaptive Time-Stepping Strategies. Symmetry. Symmetry, 15(6), 1138 (2023).

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We propose in this article a finite element approximation to study the dynamic behavior of deformable vesicles mimicking red blood cells immersed in a non-Newtonian Casson fluid with a symmetrical and regularized stress tensor. The fluid membrane, described by an implicit level set representation, follows the model of Canham-Helrich and deforms while preserving the surface inextensibility. The inextensibility constraint is managed by penalty. A two-step method with higher-order time integration is introduced based on the asymmetric composition of the discrete flow associated with the second-order backward difference formula. The framework introduces variable time steps generated using an appropriate adaptation criterion. We report several numerical simulations aimed at validating the model against existing numerical and experimental results in the case of Newtonian flow.
Preliminary results on the alteration of membrane regimes due to the non-Newtonian fluid model are provided.