  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.
