  In swimming microorganisms and the cell cytoskeleton, inextensible fibers
resist bending and twisting, and interact with the surrounding fluid to cause
or resist large-scale fluid motion. In this paper, we develop a novel numerical
method for the simulation of cylindrical fibers by extending our previous work
on inextensible bending fibers [Maxian et al., Phys. Rev. Fluids 6 (1), 014102]
to fibers with twist elasticity. In our "Euler" model, twist is a scalar
function that measures the deviation of the fiber cross section relative to a
twist-free frame, the fiber exerts only torque parallel to the centerline on
the fluid, and the perpendicular components of the rotational fluid velocity
are discarded in favor of the translational velocity. In the first part of this
paper, we justify this model by comparing it to another commonly-used
"Kirchhoff" formulation where the fiber exerts both perpendicular and parallel
torque on the fluid, and the perpendicular angular fluid velocity is required
to be consistent with the translational fluid velocity. We then develop a
spectral numerical method for the hydrodynamics of the Euler model. We define
hydrodynamic mobility operators using integrals of the Rotne-Prager-Yamakawa
tensor, and evaluate these integrals through a novel slender-body quadrature,
which requires on the order of 10 points along the fiber to obtain several
digits of accuracy. We demonstrate that this choice of mobility removes the
unphysical negative eigenvalues in the translation-translation mobility
associated with asymptotic slender body theories, and ensures strong
convergence of the fiber velocity and weak convergence of the fiber constraint
forces. We pair the spatial discretization with a semi-implicit temporal
integrator to confirm the negligible contribution of twist elasticity to the
relaxation dynamics of a bent fiber and study the instability of a twirling
fiber.
