Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies

In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose two-step time integration scheme that incorporates higher-order accuracy using asymmetric composition discrete flow based on second-order backward difference formula, followed projection onto real axis. Our framework variable steps generated appropriate adaptation criterion. validate our numerical simulations against existing experimental results case purely Newtonian flow. Furthermore, provide preliminary demonstrating influence membrane regimes.