A numerical method for inextensible elastic filaments in viscous fluids

Abstract

The deformations of flagella are important in the motility of single- and multi-flagellated bacteria. Existing numerical methods have treated flagella as extensible filaments with a large extensional modulus, resulting in a stiff numerical problem and long simulation times. However, flagella are nearly inextensible, so to avoid large extensional stiffness, we introduce inextensible elastic rod models with hydrodynamics treated by a surface distribution of regularized Stokeslets. We benchmark this new model against previously described models of extensible elastic rods with hydrodynamics treated by a centerline distribution of regularized Stokeslets and rotlets, as well as a surface distribution of regularized Stokeslets. We compare the accuracy of the inextensible model with the extensible models and illustrate for which ratios of stretching/bending stiffness (which depend on the diameter of filament) the inextensible model is accurate and more efficient. We show that our inextensible approach can be markedly more efficient than the extensible models for many biological filaments. We also compare the accuracy of the centerline distribution of the Stokeslets and rotlets to the more accurate surface distribution of Stokeslets for modeling fluid-structure interactions of filaments.