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8124 results in Fluid dynamics and solid mechanics

Page 81 of 407

  • 10 - Transition and Receptivity

  • W. O. Criminale, University of Washington, T. L. Jackson, University of Florida, R. D. Joslin
  • Book:
    Theory and Computation in Hydrodynamic Stability
    Published online:
    22 November 2018
    Print publication:
    06 December 2018, pp 287-315

  • Summary

    Chapter 10 discusses the breakdown of hydrodynamic instability theory and the transition from laminar to turbulent flow. This chapter will expose the reader to issues effecting hydrodynamic instabilities, as well as the nonlinear breakdown of modes after linear growth, ending with a summary of a condensed history of methods that have been used to predict loss of laminar flow and the onset of transition to turbulence.

  • 2 - Temporal Stability of Inviscid Incompressible Flows

  • W. O. Criminale, University of Washington, T. L. Jackson, University of Florida, R. D. Joslin
  • Book:
    Theory and Computation in Hydrodynamic Stability
    Published online:
    22 November 2018
    Print publication:
    06 December 2018, pp 26-75

  • Summary

    Chapter 2 is devoted to the temporal stability of incompressible flows. The equations of motion are linearized, and the Rayleigh and Orr–Sommerfeld equations are derived using normal mode analysis. Kelvin–Helmhotlz theory is then introduced for invisicd flows, followed by a number of important theorems related to invisicd flows such as Rayleigh’s Inflection Point Theorem, Fjotroft’s Thoerem and Howard’s Semicircle Theorem, all of which are discussed in detail. The chapter concludes with the stability of the laminar mixing layer.

  • NEW ADAPTIVE BARZILAI–BORWEIN STEP SIZE AND ITS APPLICATION IN SOLVING LARGE-SCALE OPTIMIZATION PROBLEMS

  • Part of
  • TING LI, ZHONG WAN
  • Journal:
    The ANZIAM Journal / Volume 61 / Issue 1 / January 2019
    Published online by Cambridge University Press:
    03 December 2018, pp. 76-98
    • Article
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  • We propose a new adaptive and composite Barzilai–Borwein (BB) step size by integrating the advantages of such existing step sizes. Particularly, the proposed step size is an optimal weighted mean of two classical BB step sizes and the weights are updated at each iteration in accordance with the quality of the classical BB step sizes. Combined with the steepest descent direction, the adaptive and composite BB step size is incorporated into the development of an algorithm such that it is efficient to solve large-scale optimization problems. We prove that the developed algorithm is globally convergent and it R-linearly converges when applied to solve strictly convex quadratic minimization problems. Compared with the state-of-the-art algorithms available in the literature, the proposed step size is more efficient in solving ill-posed or large-scale benchmark test problems.

Theory and Computation in Hydrodynamic Stability
  • 2nd edition
  • W. O. Criminale, T. L. Jackson, R. D. Joslin
  • Published online:
    22 November 2018
    Print publication:
    06 December 2018
  • The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most importantly, provide solutions to the numerous extended exercises.

Page 81 of 407