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
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
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
A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equat...A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.展开更多
This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） metho...This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.展开更多
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.
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.
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。
基金Supported by the National Natural Science Foundation of China(11271127)Science Research Projectof Guizhou Province Education Department(QJHKYZ[2013]207)
文摘A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.
基金Project supported by the National Natural Science Foundation of China(No.11671106)the Fundamental Research Funds for the Central Universities(No.2016MS33)
文摘This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.
