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  • 1
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    Scaling of Differential Equations (2021)
    Springer Nature | Springer International Publishing
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    Publication Date: 2024-04-04
    Description: The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
    Keywords: Ordinary Differential Equations ; Partial Differential Equations ; Mathematical Modeling and Industrial Mathematics ; Computational Science and Engineering ; Simulation and Modeling ; Analysis ; Computer Science ; scaling ; non-dimensionalization ; dimensionless numbers ; fluid mechanics ; multiphysics models ; Differential calculus & equations ; Mathematical modelling ; Maths for engineers ; Maths for scientists ; Computer modelling & simulation ; thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations ; thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling ; thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists ; thema EDItEUR::U Computing and Information Technology::UY Computer science::UYM Computer modelling and simulation
    Language: English
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  • 2
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    Scaling of Differential Equations (2021)
    Springer Nature
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    Publication Date: 2024-04-04
    Description: Differential equations; Simulation and modeling
    Keywords: Differential equations ; Simulation and modeling ; thema EDItEUR::P Mathematics and Science
    Language: English
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  • 3
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    Experiments and computation of onshore breaking solitary waves (2005)
    Institute of Physics
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    Publication Date: 2005-08-23
    Print ISSN: 0957-0233
    Electronic ISSN: 1361-6501
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Published by Institute of Physics
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  • 4
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    Optimization of acceleration measurements using PIV (2004)
    Institute of Physics
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    Publication Date: 2004-10-09
    Print ISSN: 0957-0233
    Electronic ISSN: 1361-6501
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Published by Institute of Physics
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  • 5
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    An experimental study of wave run-up at a steep beach (2003)
    Cambridge University Press
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    Publication Date: 2003-06-10
    Description: This paper presents experiments on run-up of strongly nonlinear waves on a beach of 10.54° inclination. Velocity fields are obtained by the PIV (particle image velocimetry) technique. Acceleration measurements are also attempted, but it is difficult to obtain useful results in every case. In addition, free-surface profiles are extracted from digital images and wave resistance probes. The investigation focuses on the dynamics of the early stages of the run-up, when steep fronts evolve in the vicinity of the equilibrium shoreline, but maximum run-up heights are also reported. Measurements on moderately nonlinear waves are compared to results from long-wave theories, including a numerical Boussinesq model and analytic shallow-water results from the literature. In particular the applicability of the long-wave theories is addressed. However, most attention is given to run-up of high incident solitary waves that are on the brink of breaking at the shoreline. In one case a temporarily slightly overturning wave front is found that neither develops into a plunger or displays appreciable spilling. This feature is discussed in view of measured velocity and acceleration patterns and with reference to the dam-break problem. Effects of scaling, as well as viscous damping, are also briefly discussed.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 6
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    Linear stability of boundary layers under solitary waves (2014)
    Cambridge University Press
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    Publication Date: 2014-11-14
    Description: In the present treatise, the stability of the boundary layer under solitary waves is analysed by means of the parabolized stability equation. We investigate both surface solitary waves and internal solitary waves. The main result is that the stability of the flow is not of parametric nature as has been assumed in the literature so far. Not only does linear stability analysis highlight this misunderstanding, it also gives an explanation why Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207-231), Vittori & Blondeaux (Coastal Engng, vol. 58, 2011, pp. 206-213) and Ozdemir et al. (J. Fluid Mech., vol. 731, 2013, pp. 545-578) each obtained different critical Reynolds numbers in their experiments and simulations. We find that linear instability is possible in the acceleration region of the flow, leading to the question of how this relates to the observation of transition in the acceleration region in the experiments by Sumer et al. or to the conjecture of a nonlinear instability mechanism in this region by Ozdemir et al. The key concept for assessment of instabilities is the integrated amplification which has not been employed for this kind of flow before. In addition, the present analysis is not based on a uniformization of the flow but instead uses a fully nonlinear description including non-parallel effects, weakly or fully. This allows for an analysis of the sensitivity with respect to these effects. Thanks to this thorough analysis, quantitative agreement between model results and direct numerical simulation has been obtained for the problem in question. The use of a high-order accurate Navier-Stokes solver is primordial in order to obtain agreement for the accumulated amplifications of the Tollmien-Schlichting waves as revealed in this analysis. An elaborate discussion on the effects of amplitudes and water depths on the stability of the flow is presented. © 2014 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Non-modal stability analysis of the boundary layer under solitary waves (2017)
    Cambridge University Press
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    Publication Date: 2017-12-12
    Description: In the present work, a stability analysis of the bottom boundary layer under solitary waves based on energy bounds and non-modal theory is performed. The instability mechanism of this flow consists of a competition between streamwise streaks and two-dimensional perturbations. For lower Reynolds numbers and early times, streamwise streaks display larger amplification due to their quadratic dependence on the Reynolds number, whereas two-dimensional perturbations become dominant for larger Reynolds numbers and later times in the deceleration region of this flow, as the maximum amplification of two-dimensional perturbations grows exponentially with the Reynolds number. By means of the present findings, we can give some indications on the physical mechanism and on the interpretation of the results by direct numerical simulation in Vittori & Blondeaux (J. Fluid Mech., vol. 615, 2008, pp. 433-443) and Özdemir et al. (J. Fluid Mech., vol. 731, 2013, pp. 545-578) and by experiments in Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207-231). In addition, three critical Reynolds numbers can be defined for which the stability properties of the flow change. In particular, it is shown that this boundary layer changes from a monotonically stable to a non-monotonically stable flow at a Reynolds number of Reδ = 18. © 2017 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    Oblique runup of non-breaking solitary waves on an inclined plane (2011)
    Cambridge University Press
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    Publication Date: 2011-01-26
    Description: When a wave of permanent form is obliquely incident on an inclined plane, the wave pattern becomes stationary in a frame of reference which moves along the shore. This enables a simplified mathematical description of the problem which is used herein as a basis for efficient and accurate numerical simulations. First, a nonlinear and weakly dispersive set of Boussinesq equations for the downstream evolution of such stationary patterns is derived. In the hydrostatic approximation, streamline-based Lagrangian versions of the evolution equations are developed for automatic tracing of the shoreline. Both equation sets are, in their present form, developed for non-breaking waves only. Finite difference models for both equation sets are designed. These methods are then coupled dynamically to obtain a single nonlinear model with dispersive wave propagation in finite depth and an accurate runup representation. The models are tested by runup of waves at normal incidence and comparison with a more general model for the refraction of a solitary wave on a slope. Finally, a set of runup computations for oblique solitary waves is performed and compared with estimates of oblique runup heights obtained from a combination of an analytic solution for normal incidence and optics. We find that the runup heights decrease in proportion to the square of the angle of incidence for angles up to 45°, for which the height is reduced by around 12% relative to that of normal incidence. In Appendix A, the validity of the downstream formulation is discussed in the light of solitary wave optics and wave jumps. © 2011 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    Boundary-layer flow and bed shear stress under a solitary wave: revision (2014)
    Cambridge University Press
    Details
    Publication Date: 2014-07-28
    Description: We address two shortcomings in the article by Liu, Park & Cowen (J. Fluid Mech., vol. 574, 2007, pp. 449-463), which gave a theoretical and experimental treatise of the bottom boundary-layer under a solitary wave. © 2014 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 10
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    A Boussinesq type extension of the GeoClaw model - a study of wave breaking phenomena applying dispersive long wave models (2017)
    Elsevier
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    Publication Date: 2017-04-01
    Print ISSN: 0378-3839
    Electronic ISSN: 1872-7379
    Topics: Architecture, Civil Engineering, Surveying
    Published by Elsevier
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