One-dimensional finite element grids based on a localized truncation error analysis

    Authors

    S. C. Hagen; J. J. Westerink;R. L. Kolar

    Abbreviated Journal Title

    Int. J. Numer. Methods Fluids

    Keywords

    finite elements; shallow water equations; truncation error analysis; grid generation; SHALLOW-WATER EQUATIONS; BOUNDARY-CONDITIONS; MODEL; PROGRESS; TIDES; Computer Science, Interdisciplinary Applications; Mathematics, ; Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas

    Abstract

    With the exponential increase in computing power, modelers of coastal and oceanic regions are capable of simulating larger domains with increased resolution. Typically, these models use graded meshes wherein the size of the elements can vary by orders of magnitude. However, with notably few exceptions, the graded meshes are generated using criteria that neither optimize placement of the node points nor properly incorporate the physics, as represented by discrete equations, underlying tidal flow and circulation to the mesh generation process. Consequently, the user of the model must heuristically adjust such meshes based on knowledge of local flow and topographical features--a rough and time consuming proposition at best. Herein, a localized truncation error analysis (LTEA) is proposed as a means to efficiently generate meshes that incorporate estimates of flow variables and their derivatives. In a one-dimensional (1D) setting, three different LTEA-based finite element grid generation methodologies are examined and compared with two common algorithms: the wavelength to Delta x ratio criterion and the topographical length scale criterion. Errors are compared on a per node basis. It is shown that solutions based on LTEA meshes are, in general, more accurate (both locally and globally) and more efficient. In addition, the study shows that the first four terms of the ordered truncation error series are in direct competition and, subsequently, that the leading order term of the truncation error series is not necessarily the dominant term. Analyses and results from this 1D study lay the groundwork for developing an efficient mesh generating algorithm suitable for two-dimensional (2D) models. Copyright (C) 2000 John Wiley & Sons, Ltd.

    Journal Title

    International Journal for Numerical Methods in Fluids

    Volume

    32

    Issue/Number

    2

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    241

    Last Page

    261

    WOS Identifier

    WOS:000084865100005

    ISSN

    0271-2091

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