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Quantum turbulence simulations using the Gross–Pitaevskii equation: High-performance computing and new numerical benchmarks
Computer Physics Communications ( IF 7.2 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.cpc.2020.107579
Michikazu Kobayashi , Philippe Parnaudeau , Francky Luddens , Corentin Lothodé , Luminita Danaila , Marc Brachet , Ionut Danaila

This paper is concerned with the numerical investigation of Quantum Turbulence (QT) described by the Gross-Pitaevskii (GP) equation. Numerical simulations are performed using a parallel (MPI-OpenMP) code based on a pseudo-spectral spatial discretization and second order splitting for the time integration. We start by revisiting (in the framework of high-performance/high-accuracy computations) well-known GP-QT settings, based on the analogy with classical vortical flows: Taylor-Green (TG) vortices and Arnold-Beltrami-Childress (ABC) flow. Two new settings are suggested to build the initial condition for the QT simulation. They are based on the direct manipulation of the wave function by generating a smoothed random phase (SRP) field, or seeding random vortex rings (RVR) pairs. The new initial conditions have the advantage to be simpler to implement than the TG and ABC approaches, while generating statistically equivalent QT fields. Each of these four GP-QT settings is described in detail by defining corresponding benchmarks that could be used to validate/calibrate new GP codes. We offer a comprehensive description of the numerical and physical parameters of each benchmark. We analyze the results in detail and present values, spectra and structure functions of main quantities of interest (energy, helicity, etc.) that are useful to describe the turbulent flow. Some general features of QT are identified, despite the variety of initial states.

中文翻译:

使用 Gross-Pitaevskii 方程的量子湍流模拟:高性能计算和新的数值基准

本文涉及由 Gross-Pitaevskii (GP) 方程描述的量子湍流 (QT) 的数值研究。使用基于伪光谱空间离散化和时间积分二阶分裂的并行 (MPI-OpenMP) 代码执行数值模拟。我们首先重新审视(在高性能/高精度计算的框架内)众所周知的 GP-QT 设置,基于与经典涡流的类比:Taylor-Green (TG) 涡流和 Arnold-Beltrami-Childress (ABC) ) 流。建议使用两个新设置来构建 QT 模拟的初始条件。它们基于通过生成平滑的随机相位 (SRP) 场或播种随机涡环 (RVR) 对来直接操纵波函数。新的初始条件的优点是比 TG 和 ABC 方法更容易实现,同时生成统计上等效的 QT 场。通过定义可用于验证/校准新 GP 代码的相应基准,详细描述了这四个 GP-QT 设置中的每一个。我们对每个基准的数值和物理参数进行了全面的描述。我们详细分析了结果,并给出了有助于描述湍流的主要感兴趣量(能量、螺旋度等)的当前值、光谱和结构函数。尽管初始状态多种多样,但仍确定了 QT 的一些一般特征。通过定义可用于验证/校准新 GP 代码的相应基准,详细描述了这四个 GP-QT 设置中的每一个。我们对每个基准的数值和物理参数进行了全面的描述。我们详细分析了结果,并给出了有助于描述湍流的主要感兴趣量(能量、螺旋度等)的当前值、光谱和结构函数。尽管初始状态多种多样,但仍确定了 QT 的一些一般特征。通过定义可用于验证/校准新 GP 代码的相应基准,详细描述了这四个 GP-QT 设置中的每一个。我们对每个基准的数值和物理参数进行了全面的描述。我们详细分析了结果,并给出了有助于描述湍流的主要感兴趣量(能量、螺旋度等)的当前值、光谱和结构函数。尽管初始状态多种多样,但仍确定了 QT 的一些一般特征。
更新日期:2021-01-01
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