Tree method for quantum vortex dynamics

Abstract

We present a numerical method to compute the evolution of vortex filaments in superfluid helium. The method is based on a tree algorithm which considerably speeds up the calculation of Biot-Savart integrals. We show that the computational cost scales as Nlog{(N) rather than N squared, where $N$ is the number of discretization points. We test the method and its properties for a variety of vortex configurations, ranging from simple vortex rings to a counterflow vortex tangle, and compare results against the Local Induction Approximation and the exact Biot-Savart law.

12 pages, 10 figures

References in corpus (9)

• Smoothed Particle Hydrodynamics in Astrophysics
• Characterization of reconnecting vortices in superfluid helium
• Velocity Statistics Distinguish Quantum Turbulence from Classical Turbulence
• Quantum and quasiclassical types of superfluid turbulence
• Energy Spectra of Developed Turbulencein Helium Superfluids
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• Cascade of vortex loops initiated by a single reconnection of quantum vortices
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Cited by in corpus (22)

• Introduction to quantum turbulence
• Quantum vortex reconnections
• Numerical Studies of Quantum Turbulence
• Coherent vortex structures in quantum turbulence
• Quasiclassical and ultraquantum decay of superfluid turbulence
• Thermally- and mechanically-driven quantum turbulence in helium II
• Vortex line density in counterflowing He II with laminar and turbulent normal fluid velocity profiles
• Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation
• Coherent laminar and turbulent motion of toroidal vortex bundles
• Hydrodynamic simulations of pulsar glitch recovery
• Visualizing Pure Quantum Turbulence in Superfluid ${}^3$He: Andreev Reflection and its Spectral Properties
• Local and nonlocal dynamics in superfluid turbulence
• Visualization of quantum turbulence in superfluid ${}^3$He-B: Combined numerical/experimental study of Andreev reflection
• Superfluid turbulence driven by cylindrically symmetric thermal counterflow
• Identification of Kelvin waves: numerical challenges
• Acceleration statistics in thermally driven superfluid turbulence
• Nonlocality in Homogeneous Superfluid Turbulence
• Reconnection dynamics and mutual friction in quantum turbulence
• Vortex Simulations on a 3-Sphere
• Coarse-grained pressure dynamics in superfluid turbulence
• Vorticity Locking and Pressure Dynamics in Finite-Temperature Superfluid Turbulence
• Modelling turbulent flow of superfluid ${}^4$He past a rough solid wall in the $T=0$ limit