Reproduction of vortex lattices in the simulations of rotating liquid helium-4 by numerically solving the two-fluid model using smoothed-particle hydrodynamics incorporating vortex dynamics

TL;DR

This paper presents an improved numerical simulation method for liquid helium-4 that successfully reproduces vortex lattices by explicitly modeling vortex dynamics within the two-fluid framework using smoothed-particle hydrodynamics.

Contribution

The authors develop an enhanced SPH scheme that incorporates vortex dynamics, enabling the reproduction of vortex lattices in rotating helium-4 simulations, which was not achieved in previous models.

Findings

Vortex lattices were successfully simulated with the new scheme.

The vortex count aligned with Feynman's rule after parameter optimization.

The model demonstrated vortex spinning and rigid-body rotation phenomena.

Abstract

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.