Quantum turbulence simulations using the Gross–Pitaevskii equation: High-performance computing and new numerical benchmarks

We present high-performance and high-accuracy numerical simulations of quantum turbulence modelled by the Gross–Pitaevskii equation for time-evolution macroscopic wave function system. The hydrodynamic analogue this model is a flow in which viscosity absent all rotational carried quantized vortices with identical topological line-structure circulation. Numerical start from an initial state containing large number follow chaotic vortex interactions leading to vortex-tangle turbulent state. solved using parallel (MPI-OpenMP) code based on pseudo-spectral spatial discretization second order splitting time integration. define four quantum-turbulence simulation cases different methods used generate states: first two are analogy classical Taylor–Green Arnold–Beltrami–Childress flows, while other use direct manipulation generating smoothed random phase field, or seeding vortex-ring pairs. dynamics field corresponding each case analysed detail presenting statistical properties (spectra structure functions) main quantities interest (energy, helicity, etc.). Some general features identified, despite variety states. physical parameters presented defining benchmarks that could be validate calibrate new codes. efficiency computation reference also reported.