Particle approximation of the two-fluid model for superfluid ⁴He using smoothed particle hydrodynamics

This paper presents a finite particle approximation of the two-fluid model for liquid $^4$He using smoothed hydrodynamics (SPH). In recent years, several studies have combined vortex filament (VFM), which describes quantized vortices in superfluid components, with Navier-Stokes equations, describe motion normal fluids. These led us to assume that coupling both components instead VFM component enables approximate system. this study, we formulated new SPH simultaneously solves equations model. We then performed numerical simulation rotating our SPH. The results showed two major phenomena, emergence multiple independent parallel circular axis and so-called rigid-body rotation, can be reproduced by solving finding is interesting because it was previously assumed only single emerges when addressing similar problems without considering quantum mechanics. Our further analysis found realized reformulating viscosity term conserve angular momentum particles around their axes. Consequently, succeeded reproducing phenomena observed cases, even though solve phenomenological governing $^4$He.