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    Wyświetlanie 1-3 z 3
    Tytuł:
    Balance errors in numerical solutions of shallow water equations
    Autorzy:
    Gąsiorowski, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/1933150.pdf
    Data publikacji:
    2007
    Wydawca:
    Politechnika Gdańska
    Tematy:
    shallow water equations
    nonlinear advection equations
    numerical errors
    conservation laws
    mass and momentum balance
    Opis:
    An analysis of the conservative properties of shallow water equations is presented, focused on the consistency of their numerical solution with the conservation laws of mass and momentum. Two different conservative forms are considered, solved by an implicit box scheme. Theoretical analysis supported with numerical experiments is carried out for a rectangular channel and arbitrarily assumed flow conditions. The improper conservative form of the dynamic equation is shown not to guarantee a correct solution with respect to the conservation of momentum. Consequently, momentum balance errors occur in the numerical solution. These errors occur when artificial diffusion is simultaneously generated by a numerical algorithm.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2007, 11, 4; 329-340
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation
    Autorzy:
    Gąsiorowski, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/241192.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
    Tematy:
    diffusive wave equation
    shallow water equations
    overland flow
    floodplain inundation
    finite element method
    Opis:
    A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of a moving wet-dry front, which lead to instability in numerical solutions. To overcome these difficulties, a simplified model in the form of a non-linear diffusive wave equation (DWE) can be used. The diffusive wave approach requires numerical algorithms that are much simpler, and consequently, the computational process is more effective than in the case of the SWE. In this paper, the numerical solution of the one-dimensional DWE based on the modified finite element method is verified in terms of accuracy. The resulting solutions of the DWE are compared with the corresponding benchmark solution of the one-dimensional SWE obtained by means of the finite volume methods. The results of numerical experiments show that the algorithm applied is capable of reproducing the reference solution with satisfactory accuracy even for a rapidly varied wave over a dry bottom.
    Źródło:
    Archives of Hydro-Engineering and Environmental Mechanics; 2014, 61, 3-4; 111--125
    1231-3726
    Pojawia się w:
    Archives of Hydro-Engineering and Environmental Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution of the dike-break problem using finite volume method and splitting technique
    Autorzy:
    Gąsiorowski, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/1934027.pdf
    Data publikacji:
    2011
    Wydawca:
    Politechnika Gdańska
    Tematy:
    finite volume method
    shallow water equations
    approximate Riemann solver
    dambreak
    dike-break
    wave-propagation method
    Opis:
    In this paper, an approach using the finite volume method (FVM) for the solution of two-dimensional shallow water equations is described. Such equations are frequently used to simulate dam-break and dike-break induced flows. The applied numerical algorithm of the FVM is based on a wave-propagation algorithm, which ensures a stable solution and, simultaneously, minimizes numerical errors. Dimensional decomposition according to the coordinate directions was used to split two-dimensional shallow water equations into one-dimensional equations. Additionally, splitting was also applied with respect to the physical processes. The applied dimensional and physical splitting, together with the wave-propagation algorithm led to an effective algorithm and ensured proper incorporation of source terms into the scheme of the finite volume method. A detailed description of an approximation for numerical fluxes and source terms is presented. The obtained numerical results are compared with analytical solutions, laboratory experiments and other results available in the literature.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2011, 15, 3-4; 251-270
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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