In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equ...In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equation. In addition, when the seabed interface is irregular, traditional finite-difference schemes cannot simulate the seismic wave propagation across the irregular seabed interface. Therefore, an acoustic–elastic forward modeling and vector-based P-and S-wave separation method is proposed. In this method, we divide the fluid–solid elastic media with irregular interface into orthogonal grids and map the irregular interface in the Cartesian coordinates system into a horizontal interface in the curvilinear coordinates system of the computational domain using coordinates transformation. The acoustic and elastic wave equations in the curvilinear coordinates system are applied to the fluid and solid medium, respectively. At the irregular interface, the two equations are combined into an acoustic–elastic equation in the curvilinear coordinates system. We next introduce a full staggered-grid scheme to improve the stability of the numerical simulation. Thus, separate P-and S-wave equations in the curvilinear coordinates system are derived to realize the P-and S-wave separation method.展开更多
为进一步提升高雷诺数、大迎角(Angle of attack,AoA)和高马赫数下的翼型可压缩流场预测精度和效率,本文提出了一种基于坐标转换方法和UNet神经网络的机器学习推理方法。首先,提出了用于数据前处理的坐标转换方法,将计算流体力学中的物...为进一步提升高雷诺数、大迎角(Angle of attack,AoA)和高马赫数下的翼型可压缩流场预测精度和效率,本文提出了一种基于坐标转换方法和UNet神经网络的机器学习推理方法。首先,提出了用于数据前处理的坐标转换方法,将计算流体力学中的物理量和网格信息转换成神经网络空间信息,使流场信息的分布更符合神经网络的输入要求。其次,建立了新型深度UNet神经网络,使模型学习到翼型流场精细复杂的局部流动特征。本文将两种方法结合,建立了翼型可压缩流场机器学习推理方法,得到快速高精度的推理模型。最后,对不同种类翼型的流场与气动力进行预测分析,并与传统机器学习方法预测的结果进行比较。结果表明,本文提出的机器学习推理方法能够较好地预测翼型的可压缩流场,并且能够更好地捕捉高雷诺数下的复杂流动行为以及预测大迎角、高马赫数条件下的流动分离和激波现象。展开更多
We succeed in solving quantum-mechanically the problem of a hydrogen atom in a strong magnetic field in the(r,ρ,Ф)coordinate system in which the main part of the Hamiltonian can be solved by separation of variables....We succeed in solving quantum-mechanically the problem of a hydrogen atom in a strong magnetic field in the(r,ρ,Ф)coordinate system in which the main part of the Hamiltonian can be solved by separation of variables.The theoretical energy spectrum agrees to a certain extent with the experimental one.展开更多
基金financially supported by the Natural Science Foundation of China(No.41774133)the Open Funds of SINOPEC Key Laboratory of Geophysics(No.wtyjy-wx2017-01-04)National Science and Technology Major Project of the Ministry of Science and Technology of China(No.2016ZX05024-003-011)
文摘In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equation. In addition, when the seabed interface is irregular, traditional finite-difference schemes cannot simulate the seismic wave propagation across the irregular seabed interface. Therefore, an acoustic–elastic forward modeling and vector-based P-and S-wave separation method is proposed. In this method, we divide the fluid–solid elastic media with irregular interface into orthogonal grids and map the irregular interface in the Cartesian coordinates system into a horizontal interface in the curvilinear coordinates system of the computational domain using coordinates transformation. The acoustic and elastic wave equations in the curvilinear coordinates system are applied to the fluid and solid medium, respectively. At the irregular interface, the two equations are combined into an acoustic–elastic equation in the curvilinear coordinates system. We next introduce a full staggered-grid scheme to improve the stability of the numerical simulation. Thus, separate P-and S-wave equations in the curvilinear coordinates system are derived to realize the P-and S-wave separation method.
文摘为进一步提升高雷诺数、大迎角(Angle of attack,AoA)和高马赫数下的翼型可压缩流场预测精度和效率,本文提出了一种基于坐标转换方法和UNet神经网络的机器学习推理方法。首先,提出了用于数据前处理的坐标转换方法,将计算流体力学中的物理量和网格信息转换成神经网络空间信息,使流场信息的分布更符合神经网络的输入要求。其次,建立了新型深度UNet神经网络,使模型学习到翼型流场精细复杂的局部流动特征。本文将两种方法结合,建立了翼型可压缩流场机器学习推理方法,得到快速高精度的推理模型。最后,对不同种类翼型的流场与气动力进行预测分析,并与传统机器学习方法预测的结果进行比较。结果表明,本文提出的机器学习推理方法能够较好地预测翼型的可压缩流场,并且能够更好地捕捉高雷诺数下的复杂流动行为以及预测大迎角、高马赫数条件下的流动分离和激波现象。
文摘We succeed in solving quantum-mechanically the problem of a hydrogen atom in a strong magnetic field in the(r,ρ,Ф)coordinate system in which the main part of the Hamiltonian can be solved by separation of variables.The theoretical energy spectrum agrees to a certain extent with the experimental one.
