The modal decomposition technique is one of the most effective methods for studying the flow dynamics in a complex flow. By rejuvenating the discrete Fourier transform(DFT), this paper proposes a Fourier mode decompos...The modal decomposition technique is one of the most effective methods for studying the flow dynamics in a complex flow. By rejuvenating the discrete Fourier transform(DFT), this paper proposes a Fourier mode decomposition(FMD) method for the time series of particle image velocimetry(PIV) data from the fluid field. An experimental case concerning the control of the flow around a circular cylinder by a synthetic jet positioned at the rear stagnation point is used to demonstrate the use of the FMD method. In the three different regimes where the natural shedding frequency and actuation frequency dominate respectively or simultaneously, it is found that the FMD method is capable of extracting the dynamic mode along with its amplitude and phase according to the selected characteristic frequency based on the global power spectrum. For the quasiperiodic flow phenomena presented in this particular case, the FMD method can reconstruct the original flow field using the zero-th mode and the selected mode corresponding to the characteristic frequency. Similarities and differences between the FMD method and the dynamical mode decomposition(DMD) and proper orthogonal decomposition(POD) methods are also discussed.展开更多
The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems.The use of ite...The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems.The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems.The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS.As an improvement of dishonest preconditioner(DP) strategy,updating preconditioner strategy(UP) is introduced to the field of TDS for the first time.The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices.In order to make the linear system sequence in TDS suitable for UP strategy,a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating.The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China.Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%-61% the iteration count of the GMRES when compared with the DP method in all test cases.Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11202015 and 11327202)
文摘The modal decomposition technique is one of the most effective methods for studying the flow dynamics in a complex flow. By rejuvenating the discrete Fourier transform(DFT), this paper proposes a Fourier mode decomposition(FMD) method for the time series of particle image velocimetry(PIV) data from the fluid field. An experimental case concerning the control of the flow around a circular cylinder by a synthetic jet positioned at the rear stagnation point is used to demonstrate the use of the FMD method. In the three different regimes where the natural shedding frequency and actuation frequency dominate respectively or simultaneously, it is found that the FMD method is capable of extracting the dynamic mode along with its amplitude and phase according to the selected characteristic frequency based on the global power spectrum. For the quasiperiodic flow phenomena presented in this particular case, the FMD method can reconstruct the original flow field using the zero-th mode and the selected mode corresponding to the characteristic frequency. Similarities and differences between the FMD method and the dynamical mode decomposition(DMD) and proper orthogonal decomposition(POD) methods are also discussed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60703055 and 60803019)the National High-Tech Research & Development Program of China ("863" Program) (Grant No. 2009AA01A129)+1 种基金State Key Development Program of Basic Research of China (Grant No. 2010CB951903)Tsinghua National Laboratory for Information Science and Technology (THList) Cross-discipline Foundation
文摘The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems.The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems.The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS.As an improvement of dishonest preconditioner(DP) strategy,updating preconditioner strategy(UP) is introduced to the field of TDS for the first time.The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices.In order to make the linear system sequence in TDS suitable for UP strategy,a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating.The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China.Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%-61% the iteration count of the GMRES when compared with the DP method in all test cases.Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.
