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The aim of this study is to investigate the effects of duct profile parameters cambers and angles of attack that distinguish accelerating and decelerating ducts on the flow characteristics of pump-jet. A detailed numerical analysis is carried out to compare the properties of pump-jets with different cambers and attack angles, and to explore the mutual interaction between the duct and components of pump-jet. Beforehand, the numerical methodology is validated by comparing the experiment and simulation results of the pump-jet under mooring conditions and propeller VP1304. Five cambers (f = 0.5t, 0.25t, 0, −0.25t, −0.5t) and three attack angles (α = 4°, 0°, −4°) of duct profile are considered carefully to distinguish accelerating and decelerating ducts, focusing on the propulsion performance and flow field information. The results show that the flow velocity at the outlet of the accelerating ducts is significantly higher compared to the inlet velocity, as opposed to the phenomenon produced by decelerating ducts. The variation of camber makes the internal evolution of the flow field more intuitive compared with the change of angles of attack. Further results indicate that the maximum efficiency of pump-jet drops after the modest growth as the cambers decrease, whose location shifts towards the lower advance coefficient J. The alteration of α leads to making the trend more direct and apparent for the decelerating and accelerating ducts. The high f is advantageous for the cavitation resistance of inside components, like rotor blades and stator blades. The impacts of changing α on the distribution of pressure in pump-jets with accelerating and decelerating ducts are more prominent than changing f. Moreover, the effects of both variations of f and α on the circumferential distributions of the velocity components are prominent, while there are still significant differences between these changes. Additionally, the velocity distribution at the inlet of pump-jets with decelerating ducts is higher than that at the outlet, and the velocity distribution of pump-jets with accelerating ducts presents the opposite pattern. • Contributing a comparative numerical simulation for the effect of the accelerating duct and decelerating ductdistinguished by different cambers and angles of attack. • Adopting experiment of noncavitating cases on propeller VP1304 and pump-jet with different rotator speeds under mooring conditions to verify the accuracy of the numerical simulation method. • Comparing single ducts with different cambers and angles of attack and flow characteristics of pump-jet with 2 types of ducts distinguished by different cambers and angles of attack. • Comparing and discussing the hydrodynamic performance curves, pressure distribution, and velocity distribution in pump-jet with different camber (f = 0.5t, 0.25t, 0, −0.25t, −0.5t) and angles of attack (α = 4°, 0°, −4°). [ABSTRACT FROM AUTHOR]

Abstract: We study the eigenvalues of a matrix A perturbed by a few special low-rank matrices. The perturbation is constructed from certain basis vectors of an invariant subspace of A, such as eigenvectors, Jordan vectors, or Schur vectors. We show that most of the eigenvalues of the low-rank perturbed matrix stayed unchanged from the eigenvalues of A; the perturbation can only change the eigenvalues of A that are related to the invariant subspace. Existing results mostly studied using eigenvectors with full column rank for perturbations, we generalize the results to more general settings. Applications of our results to a few interesting problems including the Google’s second eigenvalue problem are presented. [Copyright &y& Elsevier]

Abstract: We propose a block Davidson-type subspace iteration using Chebyshev polynomial filters for large symmetric/hermitian eigenvalue problem. The method consists of three essential components. The first is an adaptive procedure for constructing efficient block Chebyshev polynomial filters; the second is an inner–outer restart technique inside a Chebyshev–Davidson iteration that reduces the computational costs related to using a large dimension subspace; and the third is a progressive filtering technique, which can fully employ a large number of good initial vectors if they are available, without using a large block size. Numerical experiments on several Hamiltonian matrices from density functional theory calculations show the efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

We study Davidson-type subspace eigensolvers. Correction equations of Jacobi-Davidson and several other schemes are reviewed. New correction equations are derived. A general correction equation is constructed, existing correction equations may be considered as special cases of this general equation. The main theme of this study is to identify the essential common ingredient that leads to the efficiency of a diverse form of Davidson-type methods. We emphasize the importance of the approximate Rayleigh-quotient-iteration direction. [ABSTRACT FROM AUTHOR]