  Our recent study has shown that the representative phenomena of liquid
helium-4 rotating in a cylinder could be simulated by solving the two-fluid
model using smoothed-particle hydrodynamics (SPH) after reformulating the
viscosity to conserve the rotational angular momentum. Specifically, the
emergence of multiple parallel vortices and their rigid-body rotations were
observed in our previous SPH simulations. The reported scheme is based on a
classical approximation that assumes the fluid forces of both components and
their interactions, with the expectation of functioning as a coarse-grained
model of existing approximations that couple a microscopic model and the
Navier-Stokes equation. Based on previous studies, this paper proposes an
improved SPH scheme that explicitly incorporates vortex dynamics into SPH to
reproduce vortex lattices, which was not possible in previous studies.
Consequently, our improved scheme was observed to reproduce vortex lattices by
introducing the Magnus force and interaction forces among vortices into the
reformulated two-fluid model. The spinnings of the vortices and rigid-body
rotations were also observed. The number of vortices showed a certain agreement
with Feynman's rule after the model parameter was optimized. Notably, from a
scientific point of view, such vortex lattices are reproduced by the
classical-mechanical approximation. We hope that our model will help physicists
studying low-temperature physics find a new way of approaching this bizarre
phenomenon that has attracted attention for more than 80 years.
