Coupled dynamics of quantized vortices and normal fluid in superfluid $^4$He based on lattice Boltzmann method

TL;DR

This paper introduces a numerical approach combining vortex filament model and lattice Boltzmann method to simulate the coupled dynamics of vortices and normal fluid in superfluid helium-4, simplifying complex flow calculations.

Contribution

The paper presents a novel computational method that efficiently simulates superfluid helium-4 dynamics by integrating vortex filament modeling with lattice Boltzmann techniques.

Findings

The method accurately reproduces characteristic flow structures.

It effectively simulates thermal counterflows with boundary effects.

The approach reduces computational complexity compared to direct Navier-Stokes simulations.

Abstract

We investigate the coupled dynamics of quantized vortices and normal fluid in superfluid $^4$He at finite temperatures using a numerical approach based on the vortex filament model (VFM) and lattice Boltzmann method (LBM). The LBM allows us to simulate a fluid flow with only local operations, i .e., rather than solving the Navier--Stokes (NS) equations directly; a fluid flow is considered a convection of mesoscopic particles between sites on a lattice grid. Although the two-fluid nature of He II makes its flow complex, the particle-like treatment of the normal fluid in the LBM significantly reduces the complexity. We confirm, by comparing to results obtained with direct NS simulations, that the proposed numerical approach reproduces characteristic flow structures. We also demonstrate that the proposed computational approach is suitable for a thermal counterflow simulation with a solid boundary to elucidate a thermal boundary layer near a heater in a closed channel.