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Sliding plane formalism for aeroacoustic and adjoint-based sensitivity calculations 用于气动声学和基于邻接的灵敏度计算的滑动平面形式主义
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-04 DOI: 10.1016/j.cpc.2024.109421
Anton Glazkov , Miguel Fosas de Pando , Peter J. Schmid , Li He
This paper demonstrates a methodology for time-domain and time-accurate nonlinear, direct and adjoint simulations of unsteady flows and aeroacoustics for multi-component systems in relative motion. Here, the principal effort is directed towards mitigating the problem of distortion and contamination of the adjoint field at the moving interface, through a computationally lightweight, high-order sliding plane approach for which the adjoint equivalent is simple to obtain. This effort requires an attentive treatment of the interface conditions that surpasses the requirements of the more common forward (primary) problem. Sensitivity of a given quantity of interest from a time-varying flow with respect to a large number of parameters is then obtained through the adjoint operator, which is evaluated using nonlinear-adjoint looping. This technique is implemented using checkpointing and the PETSc TSAdjoint library and, after validation, applications including a rotor–stator interaction problem are presented.
本文展示了一种对相对运动的多组件系统的非稳态流动和气动声学进行时域和时间精确的非线性、直接和辅助模拟的方法。在这里,主要工作是通过一种计算轻量级的高阶滑动平面方法来缓解运动界面上的临界场失真和污染问题。这项工作要求对界面条件进行细致的处理,这超出了更常见的正向(主要)问题的要求。然后,通过使用非线性关节循环进行评估的邻接算子,可获得时变流中给定相关量对大量参数的敏感性。该技术使用检查点和 PETSc TSAdjoint 库实现,经过验证后,介绍了包括转子-定子相互作用问题在内的应用。
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引用次数: 0
Alternative split-step method for solving linearly coupled nonlinear Schrödinger equations 求解线性耦合非线性薛定谔方程的另一种分步法
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-29 DOI: 10.1016/j.cpc.2024.109414
Wesley B. Cardoso
In this paper we introduce an alternative method for solving linearly coupled nonlinear Schrödinger equations by using a split-step approach. This methodology involves approximating the nonlinear part of the evolution operator, allowing it to be solved exactly, which significantly enhances computational efficiency. The dispersive component is addressed using a spectral method, ensuring accuracy in the treatment of linear terms. As a reference, we compare our results with those obtained using the Runge-Kutta method implemented using a pseudo-spectral technique. Our findings indicate that the proposed split-step method achieves precision comparable to that of the Runge-Kutta method while nearly doubling computational efficiency. Numerical simulations include the evolution of a single soliton in each field and a collision between two solitons, demonstrating the robustness and effectiveness of our approach.
在本文中,我们介绍了一种利用分步法求解线性耦合非线性薛定谔方程的替代方法。这种方法涉及近似演化算子的非线性部分,使其能够精确求解,从而大大提高了计算效率。色散部分采用频谱方法处理,确保了线性项处理的准确性。作为参考,我们将我们的结果与使用伪频谱技术实现的 Runge-Kutta 方法获得的结果进行了比较。我们的研究结果表明,所提出的分步法达到了与 Runge-Kutta 方法相当的精度,同时计算效率提高了近一倍。数值模拟包括每个场中单个孤立子的演化和两个孤立子之间的碰撞,证明了我们方法的稳健性和有效性。
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引用次数: 0
NTVTOK-ML: Fast surrogate model for neoclassical toroidal viscosity torque calculation in tokamaks based on machine learning methods NTVTOK-ML:基于机器学习方法的托卡马克中新古典环状粘滞力矩计算的快速代用模型
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-29 DOI: 10.1016/j.cpc.2024.109413
X.-T. Yan , N.-N. Bao , C.-Y. Zhao , Y.-W. Sun , Y.-T. Meng , W.-Y. Zhou , N.-Y. Liang , Y.-X. Lu , Y.-F. Liang , B.-N. Wan
<div><div>The Neoclassical Toroidal Viscosity (NTV) torque is a crucial source of toroidal momentum in tokamaks, exerting significant influence on plasma instability and performance. Accurate numerical modeling of NTV torque is essential for experimental design and operation, as well as for gaining insight into the relevant physical processes. However, the time-consuming nature of NTV torque calculation poses challenges for its practical application in experiment analysis and physical investigations. In this study, we have developed NTVTOK-ML, a surrogate model for NTV torque calculation that combines the expressive power and fast inference of machine learning methods to achieve simultaneous accuracy and time efficiency. To obtain datasets for NTV torque, extensive numerical calculations using NTVTOK and MARS-F codes were performed under various plasma conditions of Experimental Advanced Superconducting Tokamak (EAST), covering a wide range of experimentally relevant parameter regimes and incorporating rich physical effects such as pitch angle scattering, full toroidal geometry, resonances, etc. For fixed magnetic perturbation case, NTVTOK-ML employs Multi-Layer Perceptron (MLP) deep neural network and eXtreme Gradient Boosting (XGBoost) ensemble learning techniques respectively. Furthermore, when considering linear plasma response effect, Convolutional Neural Network (CNN) is utilized to process two-dimensional magnetic perturbation data. The prediction accuracy of NTVTOK-ML is evaluated based on statistical metrics including coefficient of determination (<span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>), mean squared error (<em>MSE</em>), and relative error; single sample prediction ability; and generalization ability - demonstrating its reliability in NTV torque prediction tasks. Importantly, the computational time required for predicting NTV torque using our proposed approach is significantly reduced compared to the original numerical code by several orders of magnitude. Additionally, the flexibility offered by the NTVTOK-ML framework allows users to optimize model performance under specific circumstances. Overall, our developed method provides an accessible solution for rapid yet accurate prediction of NTV torque while incorporating essential physical effects - thereby facilitating real-time or inter-shot analysis in experiments as well as comprehensive multi-scale nonlinear time evolution modeling.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> NTVTOK-ML</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/thcd9fbjd5.1</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> Apache-2.0</div><div><em>Programming language:</em> Python</div><div><em>Nature of problem:</em> The traditional numerical calculation of NTV torque in tokamaks is time-consuming, which hinders real-time or inter-shot experimental analysis and multi-sca
新古典环形粘度(NTV)扭矩是托卡马克环形动量的重要来源,对等离子体的不稳定性和性能有重大影响。NTV 扭矩的精确数值建模对于实验设计和运行以及深入了解相关物理过程至关重要。然而,NTV 扭矩计算耗时较长,这给其在实验分析和物理研究中的实际应用带来了挑战。在本研究中,我们开发了 NTVTOK-ML,这是一种用于 NTV 扭矩计算的替代模型,它结合了机器学习方法的表现力和快速推理能力,可同时实现准确性和时间效率。为了获得 NTV 扭矩的数据集,在实验性先进超导托卡马克(EAST)的各种等离子体条件下,使用 NTVTOK 和 MARS-F 代码进行了大量数值计算,涵盖了与实验相关的广泛参数范围,并纳入了丰富的物理效应,如俯仰角散射、全环形几何、共振等。对于固定磁扰动情况,NTVTOK-ML 分别采用了多层感知器(MLP)深度神经网络和极梯度提升(XGBoost)集合学习技术。此外,在考虑线性等离子体响应效应时,利用卷积神经网络(CNN)处理二维磁扰动数据。NTVTOK-ML 的预测精度基于统计指标进行评估,包括判定系数 (R2)、均方误差 (MSE) 和相对误差;单样本预测能力;以及泛化能力--证明了其在 NTV 扭矩预测任务中的可靠性。重要的是,与原始数字代码相比,使用我们提出的方法预测 NTV 扭矩所需的计算时间大幅减少了几个数量级。此外,NTVTOK-ML 框架提供的灵活性允许用户在特定情况下优化模型性能。总之,我们开发的方法为快速准确地预测 NTV 扭矩提供了一种简便易行的解决方案,同时纳入了重要的物理效应--从而促进了实验中的实时或间歇分析,以及全面的多尺度非线性时间演化建模:NTVTOK-MLCPC 程序库链接到程序文件:https://doi.org/10.17632/thcd9fbjd5.1Licensing provisions:Apache-2.0 编程语言:问题性质:托卡马克中 NTV 扭矩的传统数值计算非常耗时,这阻碍了实时或间隔实验分析和多尺度非线性时间演化建模。为了加快计算速度,对物理模型进行了简化;然而,这些简化往往会在某些参数范围内造成定量或定性偏差。因此,同时实现非线性时间演化建模的准确性和高效率,对于实验设计和操作以及全面了解相关物理过程至关重要:1.2. 进行大量 NTVTOK 和 MARS-F 计算,以构建包含各种物理效应(如俯仰角散射、全环形几何和共振)的 NTV 扭矩数据集; 3. 使用无量纲方法和对数变换对数据集进行预处理。对于二维磁扰动数据,采用 CNN 进行预处理;4.基于深度神经网络或集合学习方法开发和训练机器学习模型;5.从统计指标、单样本预测能力、泛化能力和计算效率等方面评估模型性能。结果表明,NTVTOK-ML 代用模型可在未来的研究中应用于各种物理任务。
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引用次数: 0
GHW: A simulation code for gyrofluid Hasegawa-Wakatani plasma turbulence GHW:长谷川-若谷陀螺流体等离子体湍流模拟代码
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-28 DOI: 10.1016/j.cpc.2024.109412
Alexander Kendl
GHW is a gyrofluid code for computation of quasi-two-dimensional turbulence with consistent finite Larmor radius (FLR) effects in magnetized plasmas. The simulation setup allows for fundamental studies of FLR effects on isothermal resistive drift waves and turbulence, and contains the standard Hasegawa-Wakatani model in the limit of cold ions.
GHW 是一种陀螺流体代码,用于计算磁化等离子体中具有一致有限拉莫半径(FLR)效应的准二维湍流。该模拟装置可对等温阻力漂移波和湍流的有限拉莫尔半径效应进行基础研究,并包含冷离子极限下的标准长谷川-若谷(Hasegawa-Wakatani)模型。
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引用次数: 0
γ-Cascade V4: A semi-analytical code for modeling cosmological gamma-ray propagation γ-Cascade V4:模拟宇宙学伽马射线传播的半解析代码
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-28 DOI: 10.1016/j.cpc.2024.109408
Antonio Capanema , Carlos Blanco
Since the universe is not transparent to gamma rays with energies above around one hundred GeV, it is necessary to account for the interaction of high-energy photons with intergalactic radiation fields in order to model gamma-ray propagation. Here, we present a public numerical software for the modeling of gamma-ray observables. This code computes the effects on gamma-ray spectra from the development of electromagnetic cascades and cosmological redshifting. The code introduced here is based on the original γ-Cascade, and builds on it by improving its performance at high redshifts, introducing new propagation modules, and adding many more extragalactic radiation field models, which enables the ability to estimate the uncertainties inherent to EBL modeling. We compare the results of this new code to existing Monte Carlo electromagnetic transport models, finding good agreement within EBL uncertainties.
由于宇宙对能量超过一百 GeV 的伽马射线并不透明,因此有必要考虑高能光子与星际辐射场的相互作用,以建立伽马射线传播模型。在这里,我们介绍一个用于伽马射线观测数据建模的公共数值软件。该软件可以计算电磁级联和宇宙学红移对伽马射线光谱的影响。这里介绍的代码是基于最初的 γ 级联,并在此基础上改进了它在高红移下的性能,引入了新的传播模块,增加了更多的河外辐射场模型,从而能够估计 EBL 建模固有的不确定性。我们将这一新代码的结果与现有的蒙特卡洛电磁传输模型进行了比较,发现在 EBL 的不确定性范围内两者的结果非常一致。
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引用次数: 0
Performance evaluation of the LBM simulations in fluid dynamics on SX-Aurora TSUBASA vector engine 在 SX-Aurora TSUBASA 矢量发动机上进行流体动力学 LBM 仿真的性能评估
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-28 DOI: 10.1016/j.cpc.2024.109411
Xiangcheng Sun , Keichi Takahashi , Yoichi Shimomura , Hiroyuki Takizawa , Xian Wang
Currently, the lattice Boltzmann method (LBM) with high-performance computing (HPC) technologies, such as graphics processing units (GPUs), has been widely adopted to solve various complex problems in fluid dynamics. In addition to GPUs, the vector engine (VE) developed by NEC Corporation has also emerged as an effective solution for memory-intensive numerical simulations such as LBM. Consequently, it is imperative to evaluate the performance of LBM simulations accelerated by VE. This study discusses our self-developed LBM code for both classical and fused implementations on the VE. Through numerical simulations of 2D and 3D lid-driven cavity flows, the performance of the brand-new VE Type 30A (VE30) in conducting large-scale grid is evaluated and analyzed, and a comparison is made against the results obtained with VE Type 20B (VE20), NVIDIA A100 GPU (A100) and H100 GPU (H100). The results indicate that, regardless of the LBM implementation, H100 achieves the highest performance. Furthermore, owing to the substantial enhancements in VE30's memory hierarchy, the performance of the streaming kernel in the classical implementation of LBM has been significantly improved compared to VE20 and A100, approaching that of H100. However, due to the characteristic of fused implementation requiring fewer memory accesses, the performance of VE30 is inferior to that of H100 in the fused implementation. Additionally, it is anticipated that, under specific physical issues and requirements, VE30 will exhibit evident performance potential in LBM simulations with large-scale grid sizes.
目前,采用图形处理器(GPU)等高性能计算(HPC)技术的格子波尔兹曼法(LBM)已被广泛用于解决流体动力学中的各种复杂问题。除了 GPU 之外,NEC 公司开发的矢量引擎(VE)也已成为 LBM 等内存密集型数值模拟的有效解决方案。因此,评估由 VE 加速的 LBM 仿真的性能势在必行。本研究讨论了我们自主开发的 LBM 代码在 VE 上的经典实现和融合实现。通过对二维和三维顶盖驱动空腔流的数值模拟,评估和分析了全新的 VE 30A 型(VE30)在进行大规模网格中的性能,并与 VE 20B 型(VE20)、英伟达 A100 GPU(A100)和 H100 GPU(H100)获得的结果进行了比较。结果表明,无论采用哪种 LBM 实现方式,H100 的性能都是最高的。此外,由于 VE30 内存层次结构的大幅增强,经典 LBM 实现中的流内核性能与 VE20 和 A100 相比有了显著提高,接近 H100 的性能。不过,由于融合实现的特点是需要较少的内存访问,因此在融合实现中,VE30 的性能不如 H100。此外,预计在特定的物理问题和要求下,VE30 将在大规模网格尺寸的 LBM 模拟中表现出明显的性能潜力。
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引用次数: 0
Time-domain mathematical modeling of external cloak metamaterials with an unconditionally stable finite element method 用无条件稳定的有限元法建立外部隐形超材料的时域数学模型
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-28 DOI: 10.1016/j.cpc.2024.109402
Wei Wang , Yiru Liang , Meng Chen , Wei Yang
Since the cloaked object of the external cloaking device is outside the device, it is not affected by the space of the device and does not need to be wrapped with special materials, so the external cloaking device is of important research value. In this paper, a time-domain mathematical model of a cylindrical external cloaking device is constructed based on optical coordinate transformation and Lorentz dispersion model, and an unconditionally stable time-domain finite element scheme is developed to simulate the electromagnetic wave propagation in the external cloak by using a combination of the Leapfrog-ADI method and the finite element method, and the unconditional stability of the method is proved. The time-domain numerical simulations validate our theoretical analysis of the time-domain external cloaking device model and the effectiveness of the FETD method. For different incident wave irradiation, the external cloak shows different operating states, and the scattering direction maps and scattering power at different moments verify the scattering of electromagnetic field during the whole process.
由于外隐身装置的隐身对象在装置外部,不受装置空间的影响,也不需要特殊材料的包裹,因此外隐身装置具有重要的研究价值。本文基于光学坐标变换和洛伦兹色散模型,构建了圆柱形外隐身装置的时域数学模型,并建立了无条件稳定的时域有限元方案,采用 Leapfrog-ADI 法和有限元法相结合的方法模拟电磁波在外隐身装置中的传播,并证明了该方法的无条件稳定性。时域数值模拟验证了时域外部隐形装置模型的理论分析和 FETD 方法的有效性。对于不同的入射波辐照,外斗篷呈现出不同的工作状态,不同时刻的散射方向图和散射功率验证了整个过程中电磁场的散射情况。
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引用次数: 0
The MOOSE fluid properties module MOOSE 流体特性模块
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-28 DOI: 10.1016/j.cpc.2024.109407
Guillaume Giudicelli , Christopher Green , Joshua Hansel , David Andrs , April Novak , Sebastian Schunert , Benjamin Spaude , Steven Isaacs , Matthias Kunick , Robert Salko , Shane Henderson , Lise Charlot , Alexander Lindsay
The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. This paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem.

Program summary

Program title: MOOSE Fluid Properties module
CPC Library link to program files: https://doi.org/10.17632/cwzhsyp6pd.1
Developer's repository link: https://github.com/idaholab/moose/tree/next/modules/fluid_properties
Licensing provisions: LGPL
Programming language: C++, Python
Nature of problem: The simulation of thermal hydraulics of advanced nuclear reactor systems, such as heat pipe micro-reactors or molten-salt cooled pebble bed reactors, requires a wide variety of discretizations of the fluid flow equations, from 1D thermal hydraulics to computational fluid dynamics at various levels of fidelity, with a wide variety of coolants. Applications are developed within the MOOSE C++ framework by Argonne and Idaho National Laboratories to simulate these reactors for research and design purposes. These applications (Sockeye, SAM, others) rely on MOOSE for the computation of fluid properties. The fluid properties module contains properties for most advanced nuclear reactor coolants, including an interface to the Molten Salt Thermodynamics Database (MSTDB) developed by Oak Ridge National Laboratory. Single phase, two phase, and gas mixtures fluid properties are computed by the module.
Solution method: The fluid properties module includes numerous numerical methods to support the wide range of applications, notably forward automatic differentiation, conversion methods between pressure and density-driven variable sets, spline-based table lookups which are the current state of the art for the fast computation of fluid properties. The integration with MOOSE facilitates uncertainty quantification with regards to the fluid properties and optimization studies with regards to the fluid composition.
多物理场面向对象仿真环境(MOOSE)中的流体特性模块用于计算从核反应堆热水力学到地热能源等众多应用中的流体特性。这些应用推动了该模块的开发,使其能够实现多种不同的流体状态方程、具有原始和守恒流动变量的属性查询,以满足压力和密度驱动求解器的需要,以及便于扩展和维护的面向对象设计。每个流体属性都在自己的类中实现,但继承了自动微分、自动越界处理或变量转换等功能。本文介绍了该模块及其设计、用户和开发人员界面、流体和属性方面的内容以及几个应用,展示了该模块在 MOOSE 仿真生态系统中的重要作用:MOOSE 流体属性模块CPC 库与程序文件的链接:https://doi.org/10.17632/cwzhsyp6pd.1Developer's repository 链接:https://github.com/idaholab/moose/tree/next/modules/fluid_propertiesLicensing provisions:LGPL 编程语言:C++、Python问题性质:先进核反应堆系统(如热管微堆或熔盐冷却鹅卵石床反应堆)的热水力学模拟需要对流体流动方程进行多种离散化处理,从一维热水力学到不同保真度的计算流体动力学,并使用多种冷却剂。阿贡国家实验室和爱达荷国家实验室在 MOOSE C++ 框架内开发了一些应用程序,用于模拟这些反应堆,以达到研究和设计目的。这些应用程序(Sockeye、SAM 等)依靠 MOOSE 计算流体特性。流体特性模块包含大多数先进核反应堆冷却剂的特性,包括与橡树岭国家实验室开发的熔盐热力学数据库 (MSTDB) 的接口。单相、两相和气体混合物的流体特性由模块求解法计算:流体性质模块包括多种数值方法,以支持广泛的应用,特别是正向自动微分、压力和密度驱动变量集之间的转换方法、基于样条线的表格查找,这些都是当前快速计算流体性质的最先进方法。与 MOOSE 的集成有助于流体特性的不确定性量化和流体成分的优化研究。
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引用次数: 0
SU2-COOL: Open-source framework for non-ideal compressible fluid dynamics SU2-COOL:非理想可压缩流体动力学开源框架
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-28 DOI: 10.1016/j.cpc.2024.109394
Peng Yan , Giulio Gori , Marta Zocca , Alberto Guardone
We present a fully open-source framework for the numerical simulation of Non-Ideal Compressible Fluid Dynamics (NICFD). The open-source Computational Fluid Dynamics suite SU2 is coupled to the open-source thermophysical library CoolProp, which includes state-of-the-art thermodynamic models of numerous pure fluids and mixtures relevant to applications. Accurate thermodynamic models are needed due to non-ideal operating conditions in which the fluid thermodynamics cannot be described by the simple ideal-gas law (Pv=RT). The coupling interface implements new C++ classes, which allow the automatic exchange of information between SU2 and CoolProp, and it is made directly available as an additional module integrated into the open-source SU2 suite. To assess the performance of the NICFD simulation framework, we present three test cases: a nozzle flow exhibiting non-ideal thermodynamics effects, a nozzle flow with non-monotone Mach number variation, a representative non-ideal gasdynamics effect, and a non-classical rarefaction oblique shock over a wedge. Results are verified against available experiment data and solutions obtained with different implementations of non-ideal thermodynamics in SU2. Performance of the new framework is assessed on user-friendliness, scalability, solution accuracy, and computational efficiency.
我们为非理想可压缩流体动力学(NICFD)的数值模拟提出了一个完全开源的框架。开源计算流体动力学套件 SU2 与开源热物理库 CoolProp 相结合,后者包含与应用相关的众多纯流体和混合物的最新热力学模型。在非理想运行条件下,流体热力学无法用简单的理想气体定律(Pv=RT)来描述,因此需要精确的热力学模型。耦合接口实现了新的 C++ 类,允许在 SU2 和 CoolProp 之间自动交换信息,并可作为集成到开源 SU2 套件中的附加模块直接使用。为了评估 NICFD 仿真框架的性能,我们提出了三个测试案例:表现出非理想热力学效应的喷嘴流、具有非单调马赫数变化的喷嘴流、具有代表性的非理想气体动力学效应以及楔形上的非经典稀释斜冲击。研究结果与现有实验数据以及在 SU2 中采用不同非理想热力学方法获得的解决方案进行了验证。在用户友好性、可扩展性、求解精度和计算效率方面对新框架的性能进行了评估。
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引用次数: 0
Moshinsky brackets for a wide range of quantum numbers using generating functions 使用生成函数求大范围量子数的莫辛斯基括号
IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-10-26 DOI: 10.1016/j.cpc.2024.109409
Aziz H. Fatah, Adil M. Hussein, Hawar M. Dlshad
<div><div>We used a new Python code to reproduce the brackets for the Moshinsky harmonic oscillator, which was based on the generating function. We made these brackets by transforming the wave functions of two groups of coupled particle harmonic oscillators, <span><math><msubsup><mrow><mi>Φ</mi></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>l</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>Λ</mi></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>λ</mi></mrow></msubsup><mrow><mo>(</mo><msub><mrow><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></math></span> and <span><math><msubsup><mrow><mi>Φ</mi></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>a</mi></mrow></msub><msub><mrow><mi>l</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>b</mi></mrow></msub><msub><mrow><mi>l</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>,</mo><mi>Λ</mi></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>,</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>,</mo><mi>λ</mi></mrow></msubsup><mrow><mo>(</mo><msub><mrow><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow><mrow><mi>a</mi></mrow></msub><mo>,</mo><msub><mrow><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow><mrow><mi>b</mi></mrow></msub><mo>)</mo></mrow></math></span>. To convert between the supplied position and momentum coordinates in both frames, we performed orthogonal transformations on nuclei with both low and high angular momentum.</div><div>In our derivation, we have used the expansion of the generating functions <span><math><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mover><mrow><mi>p</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>.</mo><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>−</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msup></math></span> and <span><math><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>c</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>.</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></msup></math></span> in spherical coordinates in terms of harmonic oscillator wave functions. When we modified the Moshinsky brackets for two-coupled oscillator states, we used generating functions with two variables. The number of indices has significantly decreased compared to the oscillator brackets in previous references; this reduction in the program code's iterative process has yielded influential results. Compared to the previous
我们使用新的 Python 代码重现了基于生成函数的莫辛斯基谐振子的括号。我们通过变换两组耦合粒子谐振子的波函数,即Φn1l1,n2l2,Λm1,m2,λ(r→1,r→2)和Φnala,nblb,Λma,mb,λ(r→a,r→b),制作了这些括号。在推导过程中,我们使用了球面坐标中的生成函数 e2p→.r→-p2 和 e2cpi.pj 在谐振子波函数方面的展开。当我们为双耦合振荡器状态修改莫辛斯基括号时,我们使用了具有两个变量的生成函数。与之前参考文献中的振荡器括号相比,指数数量明显减少;程序代码迭代过程的减少产生了有影响力的结果。与之前版本的莫辛斯基括号代码相比,新的 Python 代码更易于使用。我们的方法就是利用这段代码来评估量子数范围广泛的莫辛斯基括号。根据启示,在生成函数中添加更多变量会使对高体相互作用起作用的莫辛斯基括号的数量增加:GFBRACKETSCPC 程序文件库链接:https://doi.org/10.17632/jvbnwp35rm.1Licensing provisions:MIT编程语言:PythonSupplementary material:问题性质:生成函数用于获得单个粒子振荡器状态的简明表示。这样做是为了制定和计算广义版的莫辛斯基括号和双体算子的矩阵元素。通过扩大基振荡态集,就有可能涵盖涉及两个以上物体的相互作用。使用扩展生成函数计算高量子数的莫辛斯基括号,可以轻松实现这一目标:Python 代码所需的迭代次数少于通过生成函数方法生成的类似代码:在计算大量子数的莫辛斯基括号时,会出现一些限制。在形成反应势时,没有量子数大于 10 的数据。此外,可以使用转换矩阵在双粒子谐振子基础上从单粒子坐标转换到质量中心坐标。即使两个粒子的质量不相等,这种转换也适用。
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We made these brackets by transforming the wave functions of two groups of coupled particle harmonic oscillators, &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. To convert between the supplied position and momentum coordinates in both frames, we performed orthogonal transformations on nuclei with both low and high angular momentum.&lt;/div&gt;&lt;div&gt;In our derivation, we have used the expansion of the generating functions &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; in spherical coordinates in terms of harmonic oscillator wave functions. When we modified the Moshinsky brackets for two-coupled oscillator states, we used generating functions with two variables. The number of indices has significantly decreased compared to the oscillator brackets in previous references; this reduction in the program code's iterative process has yielded influential results. Compared to the previous ","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"307 ","pages":"Article 109409"},"PeriodicalIF":7.2,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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Computer Physics Communications
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