A finite volume-based Eulerian–Lagrangian framework for single quantized vortex dynamics in superfluid helium

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Abstract
Simulating individual quantized vortices in superfluid helium in the presence of localized boundaries presents significant computational challenges. This paper develops a finite-volume method (FVM) implementation based on Open-source Field Operation And Manipulation for existing mesoscopic vortex-filament coupling formulations in spatially non-uniform fields. The solver incorporates the one-way vortex filament method, the traditional two-way (2W) coupling model, and the fully self-consistent two-way formulation within a unified Eulerian–Lagrangian workflow. Leveraging the geometric versatility of the FVM, the implementation accommodates complex non-conformal boundaries and synthesizes mass-conserving background potential flows. To improve the numerical robustness of the Lagrangian filament evolution without artificial geometric shrinkage, we integrate a Taubin λ−μ smoothing algorithm for spatial regularization. After benchmarking algorithmic fidelity against the intrinsic decay of bare and particle-decorated vortex rings, we investigate the symmetry-breaking kinematics of a single vortex traversing a localized thermal counterflow. Numerical results reveal that macroscopic spatial shear imposes an asymmetric mutual friction distribution on the vortex. This differential drag induces unequal descent velocities across the filament, tilting the orbital plane of the ring. The resulting reorientation of the self-induced velocity overcomes the local background superfluid advection, driving a continuous lateral drift that achieves a transverse displacement of 0.186 mm within 0.5 s. A mutual-friction dissipation analysis shows that this non-uniform trajectory reduces the length-normalized dissipation rate by 55.1% and the accumulated mutual-friction work by 30.4% relative to the uniform-counterflow case.
Funding Information
  • National Natural Science Foundation of China (No. 52206028)
  • National Natural Science Foundation of China (No. 52441601)
  • Natural Science Foundation of Zhejiang Province (No. LZ25E060002)
  • Fundamental Research Funds for the Central Universities (No. K20250227)

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