  Anisotropic particles are often encountered in different fields of soft
matter and complex fluids. In this work, we present an implementation of the
coupled hydrodynamics of solid ellipsoidal particles and the surrounding fluid
using the lattice Boltzmann method. A standard link-based mechanism is used to
implement the solid-fluid boundary conditions. We develop an implicit method to
update the position and orientation of the ellipsoid. This exploits the
relations between the quaternion which describes the ellipsoid's orientation
and the ellipsoid's angular velocity to obtain a stable and robust dynamic
update. The proposed algorithm is validated by looking at four scenarios: (i)
the steady translational velocity of a spheroid subject to an external force in
different orientations, (ii) the drift of an inclined spheroid subject to an
imposed force, (iii) three-dimensional rotational motions in a simple shear
flow (Jeffrey's orbits), and (iv) developed fluid flows and self-propulsion
exhibited by a spheroidal microswimmer. In all cases the comparison of
numerical results showed good agreement with known analytical solutions,
irrespective of the choice of the fluid properties, geometrical parameters, and
lattice Boltzmann model, thus demonstrating the robustness of the proposed
algorithm.
