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Our recent study has shown that the representative phenomena of liquidhelium-4 rotating in a cylinder could be simulated by solving the two-fluidmodel using smoothed-particle hydrodynamics (SPH) after reformulating theviscosity to conserve the rotational angular momentum. Specifically, theemergence of multiple parallel vortices and their rigid-body rotations wereobserved in our previous SPH simulations. The reported scheme is based on aclassical approximation that assumes the fluid forces of both components andtheir interactions, with the expectation of functioning as a coarse-grainedmodel of existing approximations that couple a microscopic model and theNavier-Stokes equation. Based on previous studies, this paper proposes animproved SPH scheme that explicitly incorporates vortex dynamics into SPH toreproduce vortex lattices, which was not possible in previous studies.Consequently, our improved scheme was observed to reproduce vortex lattices byintroducing the Magnus force and interaction forces among vortices into thereformulated two-fluid model. The spinnings of the vortices and rigid-bodyrotations were also observed. The number of vortices showed a certain agreementwith Feynman's rule after the model parameter was optimized. Notably, from ascientific point of view, such vortex lattices are reproduced by theclassical-mechanical approximation. We hope that our model will help physicistsstudying low-temperature physics find a new way of approaching this bizarrephenomenon that has attracted attention for more than 80 years.

physics of fluids

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