domingo, 20 de diciembre de 2009

Erratum to: Multiple positive solutions for time scale boundary value problems on infinite intervals


Erratum to: Multiple positive solutions for time scale boundary value problems on infinite intervals


  • Content Type Journal Article
  • Category Erratum
  • DOI 10.1007/s10440-009-9557-7
  • Authors

    • Xiangkui Zhao, Beijing Institute of Technology Department of Mathematics Beijing 100081 People’s Republic of China
    • Weigao Ge, Beijing Institute of Technology Department of Mathematics Beijing 100081 People’s Republic of China





Acceleration techniques for the iterative resolution of the Richards equation by the finite volume method


Groundwater flow in variably saturated soils is described by the nonlinear Richards' equation. The mass-conservative finite volume discretization recently proposed in (Adv. Water Resour. 2004; 27:1199-1215) produces a nonlinear algebraic problem, whose resolution demands for the application of an appropriate iterative strategy, such as the Picard or the Newton scheme. The Picard iterative technique results in a robust fixed-point method, which is globally convergent at a linear or sub-linear rate. On the other hand, the Newton iterative technique shows better convergence rates, but the computational cost of the full calculation is still comparable to the one of the Picard schemes, due to the additional calculation of the Jacobian matrix and its formal inversion. In this work, we investigate two acceleration techniques to reduce the cost of Newton iterations. These techniques are respectively based on a linearization of the nonlinear Jacobian matrix in accordance with the quasi-Newton approach and on a Broyden-type rank-one correction for a fixed number of sub-iterations. Numerical experiments on a set of two-dimensional test case modeling the uptake of plant roots in a highly heterogeneous soil show the performance and the effectiveness of both acceleration schemes in comparison with the original Picard and Newton methods. Copyright © 2009 John Wiley & Sons, Ltd.



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Published by xFruits
Original source : http://dx.doi.org/10.1002%2Fcnm.1364...

Numerical modelling and flow analysis of a centrifugal pump running as a turbine: Unsteady flow structures and its effects on the global performance


The purpose of this paper is to investigate the flow patterns in a centrifugal pump when it works as a centripetal turbine, with special interest in the unsteady behavior in order to explain the shape of the performance curves. Also, we focus on the determination of the radial thrust and other mechanical loads over a pump-designed machine. The pump studied is commercial, with single axial suction and a vaneless spiral volute casing.A numerical study has been carried out in order to obtain more information about the flow into the volute and the impeller. A numerical three-dimensional unsteady simulation has been developed using a commercial code that solves the URANS set of equations with a standard k-[epsiv] turbulence model. The results show the non-axisymmetric flow developed in the volute, responsible for a significant radial thrust; the interaction between the tongue and the impeller, generating force fluctuations; the velocity and pressure distributions inside the impeller; and the exit flow, characterized with post-rotation and low-pressure. These flow results allow us to understand the behavior of the machine by comparing it with the pump mode. Complementarily, an experimental study was conducted to validate the numerical model and characterize the pump-turbine performance curves at constant head. Fast-response pressure taps and a three-hole pneumatic pressure probe were employed to obtain a complete data set of non-stationary and stationary measurements throughout the centrifugal machine. As a result, loss of efficiency or susceptibility to cavitation, detected numerically, was confirmed experimentally.The study demonstrates that the numerical methodology presented here has shown its reliability and possibilities to predict the unsteady flow and time-mean characteristics of centrifugal pumps working as turbines. In particular, it is shown that the commercial design of the pump allows a reasonable use of the impeller as a turbine runner, due to the suitable adaptation of the inflow distributions to the volute casing. Moreover, the efficiency for the inverse mode is shown to be as high as achieved for the pumping operational mode. In addition, it is concluded that both axial and radial thrusts are controlled, though important unsteady fluctuations - up to 25% - clocked with the blade passing frequency appear beyond the nominal conditions. In that case, a moderate use of the pump as a turbine is recommended in order to minimize risks of fatigue failure of the bearings. Copyright © 2009 John Wiley & Sons, Ltd.



Published by
Published by xFruits
Original source : http://dx.doi.org/10.1002%2Ffld.2201...

Matrix interpretation of multiple orthogonality





Multiple Level Sets for Piecewise Constant Surface Reconstruction in Highly Ill-Posed Problems