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

被引:10
作者
Kobayashi, Michikazu [1 ]
Parnaudeau, Philippe [2 ]
Luddens, Francky [3 ]
Lothode, Corentin [3 ]
Danaila, Luminita [4 ]
Brachet, Marc [5 ]
Danaila, Ionut [3 ]
机构
[1] Kochi Univ Technol, Sch Environm Sci & Engn, Kami, Japan
[2] Univ Poitiers ISAE ENSMA UPR 3346, Inst Pprime, CNRS, 11 Blvd Marie & Pierre Curie, F-86962 Futuroscope, France
[3] Univ Rouen Normandie, Lab Math Raphael Salem, CNRS UMR 6085, Ave Univ,BP 12, F-76801 St Etienne Du Rouvray, France
[4] Univ Rouen Normandie, CORIA, CNRS UMR 6614, Ave Univ,BP 12, F-76801 St Etienne Du Rouvray, France
[5] Univ PSL, Sorbonne Univ, Univ Paris, Lab Phys,Ecole Normale Super,ENS,CNRS, F-75005 Paris, France
关键词
Quantum Turbulence; Gross-Pitaevskii equation; Taylor-Green; ABC; Parallel computing; Spectral method; GROUND-STATE; KOLMOGOROV TURBULENCE; MATLAB TOOLBOX; DYNAMICS; TEMPERATURE; VORTICES; GPELAB;
D O I
10.1016/j.cpc.2020.107579
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
We present high-performance and high-accuracy numerical simulations of quantum turbulence modelled by the Gross-Pitaevskii equation for the time-evolution of the macroscopic wave function of the system. The hydrodynamic analogue of this model is a flow in which the viscosity is absent and all rotational flow is carried by quantized vortices with identical topological line-structure and circulation. Numerical simulations start from an initial state containing a large number of quantized vortices and follow the chaotic vortex interactions leading to a vortex-tangle turbulent state. The Gross-Pitaevskii equation is solved using a parallel (MPI-OpenMP) code based on a pseudo-spectral spatial discretization and second order splitting for the time integration. We define four quantum-turbulence simulation cases based on different methods used to generate initial states: the first two are based on the hydrodynamic analogy with classical Taylor-Green and Arnold-Beltrami-Childress vortex flows, while the other two methods use a direct manipulation of the wave function by generating a smoothed random phase field, or seeding random vortex-ring pairs. The dynamics of the turbulent field corresponding to each case is analysed in detail by presenting statistical properties (spectra and structure functions) of main quantities of interest (energy, helicity, etc.). Some general features of quantum turbulence are identified, despite the variety of initial states. Numerical and physical parameters of each case are presented in detail by defining corresponding benchmarks that could be used to validate or calibrate new Gross-Pitaevskii codes. The efficiency of the parallel computation for a reference case is also reported. (C) 2020 Elsevier B.V. All rights reserved.
引用
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页数:26
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