A monolithic fluid-structure algorithm applied to buckling of red blood cell membrane

A parallel monolithic uid-structure interaction (FSI) algorithm presented in [Eken and Sahin, A parallel monolithic algorithm for the numerical simulation of large scale uid structure interaction problems. International Journal for Numerical Methods in Fluids, 80:687-714, (2016)] has been used to investigate the deformation of red blood cells (RBCs) in small capillaries, where cell deformability has signi cant effects on blood rheology. The method employs the divergence-free side-centered unstructured nite volume method based on Arbitrary Lagrangian-Eulerian (ALE) formulation for the uid domain and the classical Galerkin finite element formulation for the Saint Venant-Kirchhoff material in a Lagrangian frame for the solid domain. The compatible kinematic boundary condition is utilized at the uid-solid interface in order to conserve the mass of cytoplasmic uid within the red cell membrane at machine precision. The resulting large scale algebraic equations are solved in a fully coupled manner using a new matrix factorization similar to that of the projection method and the parallel algebraic multigrid solver BoomerAMG provided by the HYPRE library is used for the blocks corresponding to the scaled discrete Laplacian and the diagonal blocks of the elasticity equation. The numerical simulations initially indicate a complex shape deformation in which biconcave discoid shape changes to a parachute-like shape and then the parachute-like cell shape undergoes a cupcake shaped buckling instability for a relatively small capillarity diameter (10µm). The instability forms thin rib-like features and the red cell deformation is not axisymmetric but three-dimensional. The azimuthal wavenumber of the instability is also relatively high and it is computationally challenging to resolve.