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  • Dispersion analysis  (1)
  • Numerical Methods and Modeling  (1)
  • Tides  (1)
  • 1
    Digitale Medien
    Digitale Medien
    The influence of normal flow boundary conditions on spurious modes in finite element solutions to the shallow water equations (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1021-1060 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Finite elements ; Shallow water equations ; Boundary conditions ; Dispersion analysis ; Spurious modes ; Wave equation ; Primitive equations ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: Finite element solutions of the primitive equation (PE) form of the shallow water equations are notorious for the severe spurious 2Δx modes which appear. Wave equation (WE) solutions do not exhibit these numerical modes. In this paper we show that the severe spurious modes in PE solutions are strongly influenced by essential normal flow boundary conditions in the coupled continuity-momentum system of equations. This is demonstrated through numerical examples that avoid the use of essential normal flow boundary conditions either by specifying elevation values over the entire boundary or by implementing natural flow boundary conditions in the weak weighted residual form of the continuity equation. Results from a series of convergence tests show that PE solutions are of nearly the same quality as WE solutions when spurious modes are suppressed by alternative specification of the boundary conditions. Network intercomparisons indicate that varying nodal support does not excite spurious modes in a solution, although it does enhance the spurious modes introduced when an essential normal flow boundary condition is used.Dispersion analysis of discrete equations for interior and boundary nodes offers an explanation of the observed solution behaviour. For certain PE algorithms a mixed situation can arise where the boundary nodes exhibit a monotonic (noise-free) dispersion relationship and the interior nodes exhibit a folded (noisy) dispersion relationship. We have found that the mixed situation occurs when all boundary nodes are specified elevation nodes (which are enforced as essential conditions in the continuity equation) or when specified flow boundary nodes are treated as natural boundary conditions in the continuity equation. In either case the effect is to generate a solution that is essentially free of noise. Apparently, the monotonic dispersion behaviour at the boundaries suppresses the otherwise noisy behaviour caused by the folded dispersion relation on the interior.
    Zusätzliches Material: 18 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650181103
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  • 2
    Digitale Medien
    Digitale Medien
    A frequency-time domain finite element model for tidal circulation based on the least-squares harmonic analysis method (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 813-843 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Shallow Water Equations ; Iterative ; Harmonic Analysis ; Least Squares ; Finite Element ; Tides ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: An iterative type harmonic finite element model is developed for solving the full non-linear form of the shallow water equations. The scheme iteratively updates time histories of the non-linear terms which are then harmonically decomposed and used as forcing terms for the linear sets of equations which result from the harmonic separation of the shallow water equations.A least-squares harmonic analysis procedure is used to decompose the non-linear forcing terms. This procedure allows for the very efficient separation of extremely closely spaced harmonics, since it is highly selective with respect to the frequencies it considers. In addition tailoring the procedure and using very specific time steps and sampling periods significantly reduces the number of time samplings points required. In conjunction with the iterative nature of our scheme, the least-squares procedure makes the scheme entirely general, allows for the direct assessment of all tidal constituents, including compound tides, and permits the clear cut and complete investigation of their mutual interaction through the non-linearities. In addition this procedure readily computes very-low-frequency or residual type circulations.The FE formulation used shows a very low degree of spurious oscillations while remaining quite simple to implement. This control on nodal oscillations is especially important due to the energy transfer mechanisms involved in this type of iterative scheme.In an example application the effects of the various non-linear overtide and compound tide type interactions are examined. It is demonstrated that not only are compound tides significant relative to the overtides, but they also influence the overtides.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650080706
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  • 3
    Digitale Medien
    Digitale Medien
    Grid convergence studies for the prediction of hurricane storm surge (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 369-401 
    Details
    ISSN: 0271-2091
    Schlagwort(e): storm surge ; shallow water model ; grid convergence ; coastal ocean ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: The focus of this paper is a systematic determination of the relationship between grid resolution and errors associated with computations of hurricane storm surge. A grid structure is sought that provides the spatial resolution necessary to capture pertinent storm surge physics and does not overdiscretize. A set of numerical experiments simulating storm surge generation over 14 grid discretizations of idealized domains examines the influence of grid spacing, shoreline detail, coastline resolution and characteristics of the meteorological forcing on storm surge computations. Errors associated with a given grid are estimated using a Richardson-based error estimator. Analysis of the magnitude and location of estimated errors indicates that underresolution on the continental shelf leads to significant overprediction of the primary storm surge. In deeper waters, underresolution causes smearing or damping of the inverted barometer forcing function, which in turn results in underprediction of the surge elevation. In order to maintain a specified error level throughout the duration of the storm, the highest grid resolution is required on the continental shelf and particularly in nearshore areas. The disparity of discretization requirements between deep waters and coastal regions is best met using a graded grid. Application of the graded gridding strategy to the hindcast of Hurricane Camille reinforces the necessity of using a grid that has high levels of resolution in nearshore regions and areas of complex coastal geometry. © 1998 John Wiley & Sons, Ltd.
    Zusätzliches Material: 14 Ill.
    Materialart: Digitale Medien
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