The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The b...The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.展开更多
Time-resolved particle image velocimetry(TRPIV) experiments are performed to investigate the coherent structure's performance of riblets in a turbulent boundary layer(TBL) at a friction Reynolds number of 185. To...Time-resolved particle image velocimetry(TRPIV) experiments are performed to investigate the coherent structure's performance of riblets in a turbulent boundary layer(TBL) at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures(CSs) over a smooth surface and riblets, the proper orthogonal decomposition(POD) and finite-time Lyapunov exponent(FTLE) are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.展开更多
The reduced-order model (ROM) for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition (POD) and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are base...The reduced-order model (ROM) for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition (POD) and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes (N-S) equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation (DNS) results, the proposed model predicts flow dynamics (e.g., dominant frequency and amplitude) accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.展开更多
Proper Orthogonal Decomposition (POD) provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition (CPOD) is presented as an innovati...Proper Orthogonal Decomposition (POD) provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition (CPOD) is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.展开更多
The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are ...The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.展开更多
A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body ...A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.展开更多
The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational ...The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar). Owing to the applications of the sparse processing and EOF decomposition techniques, the computational costs of this proposed sparse flow-adaptive moderation(SFAM) localization scheme are significantly reduced. The effectiveness of PODEn4 DVar with SFAM localization is demonstrated by using the Lorenz-96 model in comparison with the Smoothed ENsemble Correlations Raised to a Power(SENCORP) and static localization schemes, separately. The performance of PODEn4 DVar with SFAM localization shows a moderate improvement over the schemes with SENCORP and static localization, with low computational costs under the imperfect model.展开更多
Over the recent years there has been an increased trend in the use of Reduced Order Models (ROM) for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method (POD)...Over the recent years there has been an increased trend in the use of Reduced Order Models (ROM) for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method (POD) has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.展开更多
针对当前油浸式电力变压器绕组瞬态温升仿真中,采用固定时间步长效率低的问题,提出一种混合变步长方法。首先,采用初始解优化算法,有效减少计算过程中方程的迭代次数;其次,结合本征正交分解算法(properorthogonal decomposition,POD),...针对当前油浸式电力变压器绕组瞬态温升仿真中,采用固定时间步长效率低的问题,提出一种混合变步长方法。首先,采用初始解优化算法,有效减少计算过程中方程的迭代次数;其次,结合本征正交分解算法(properorthogonal decomposition,POD),改善大规模有限元方程组存在的阶数过高、条件数过大的问题,提高了方程的求解效率和数值稳定性;第三,提出自适应(adaptivetimestepping,ATS)-启发式(heuristic time stepping,HTS)混合变步长算法,通过对时间步长的自适应与启发式调整,有效解决瞬态计算中计算效率与计算精度的对立问题;最后,建立油浸式电力变压器绕组二维单分区分匝的流热耦合仿真模型,以验证所提算法的正确性与高效性。数值计算结果表明:在流场中,与固定步长的计算结果相比,混合变步长算法的误差小于0.46%,计算效率提升了18.45倍;在温度场中,与固定步长的计算结果相比,所提算法的误差小于0.04%,计算效率提升了6倍。同时,通过与传统变步长算法的计算结果对比,说明所提混合变步长算法在计算精度、计算效率及变步长效果方面均具有一定优势。此外,还探讨混合变步长计算中,不同的参数设置对瞬态计算结果及状态变化过程的影响,为其工程应用奠定了一定基础。展开更多
基金This work was supported by Natural Science Basic Research Program of Shaanxi(Program No.2023-JC-YB-269)the National Natural Science Foundation of China(Grant No.41974122).
文摘The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11332006,11732010,11572221,and 11502066)the Natural Science Foundation of Tianjin City(Grant No.18JCQNJC5100)
文摘Time-resolved particle image velocimetry(TRPIV) experiments are performed to investigate the coherent structure's performance of riblets in a turbulent boundary layer(TBL) at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures(CSs) over a smooth surface and riblets, the proper orthogonal decomposition(POD) and finite-time Lyapunov exponent(FTLE) are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.
基金Project supported by the National Natural Science Foundation of China(Nos.11232011,11402262,11572314,and 11621202)
文摘The reduced-order model (ROM) for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition (POD) and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes (N-S) equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation (DNS) results, the proposed model predicts flow dynamics (e.g., dominant frequency and amplitude) accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.
基金Research Fund for Communications in Western China Under Grant No. 200431800028
文摘Proper Orthogonal Decomposition (POD) provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition (CPOD) is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.
基金National Natural Science Foundation of China (No.10671153)
文摘The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.
基金Acknowledgements The authors are grateful for the support of this research by the Committee of National Science Foundation of China (50908077) and Foundation of Heilongjiang Province Educational Committee (11551368).
文摘A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.
基金partially supported by the National High Technology Research and Development Program of China (Grant No. 2013AA122002)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX2EW-QN207)the Special Fund for Meteorological Scientific Research in the Public Interest (Grant No. GYHY201306045)
文摘The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar). Owing to the applications of the sparse processing and EOF decomposition techniques, the computational costs of this proposed sparse flow-adaptive moderation(SFAM) localization scheme are significantly reduced. The effectiveness of PODEn4 DVar with SFAM localization is demonstrated by using the Lorenz-96 model in comparison with the Smoothed ENsemble Correlations Raised to a Power(SENCORP) and static localization schemes, separately. The performance of PODEn4 DVar with SFAM localization shows a moderate improvement over the schemes with SENCORP and static localization, with low computational costs under the imperfect model.
文摘Over the recent years there has been an increased trend in the use of Reduced Order Models (ROM) for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method (POD) has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.
文摘针对当前油浸式电力变压器绕组瞬态温升仿真中,采用固定时间步长效率低的问题,提出一种混合变步长方法。首先,采用初始解优化算法,有效减少计算过程中方程的迭代次数;其次,结合本征正交分解算法(properorthogonal decomposition,POD),改善大规模有限元方程组存在的阶数过高、条件数过大的问题,提高了方程的求解效率和数值稳定性;第三,提出自适应(adaptivetimestepping,ATS)-启发式(heuristic time stepping,HTS)混合变步长算法,通过对时间步长的自适应与启发式调整,有效解决瞬态计算中计算效率与计算精度的对立问题;最后,建立油浸式电力变压器绕组二维单分区分匝的流热耦合仿真模型,以验证所提算法的正确性与高效性。数值计算结果表明:在流场中,与固定步长的计算结果相比,混合变步长算法的误差小于0.46%,计算效率提升了18.45倍;在温度场中,与固定步长的计算结果相比,所提算法的误差小于0.04%,计算效率提升了6倍。同时,通过与传统变步长算法的计算结果对比,说明所提混合变步长算法在计算精度、计算效率及变步长效果方面均具有一定优势。此外,还探讨混合变步长计算中,不同的参数设置对瞬态计算结果及状态变化过程的影响,为其工程应用奠定了一定基础。