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    Tytuł:
    Numerical simulation of rapidly varied water flow in the "Wild River" type water slide
    Autorzy:
    Burzyński, K.
    Szydłowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/241412.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
    Tematy:
    rapidly varied flow
    water slide
    mathematical modelling
    shallow water equations
    finite volume method
    Opis:
    The numerical analysis of the water flow along the 'Wild River' type water slide is presented. As the mathematical model of the free surface flow shallow water equations are assumed. In order to solve the equations, when transient, rapidly varied flow is present, the numerical scheme based on finite volume method is applied. The numerical simulation of water slide flow is computed on unstructured, triangular mesh. The results of calculation are examined against flow parameters observed on the real object installed in water park in Sopot. Generally good agreement between measured and calculated results was observed. Moreover, the calculations are compared to experimental data available due to physical modelling. As the similarity between physical phenomena of flow within water slide and in the river valley after dam-break event is observed, the investigation was realized within the framework of the State Committee for Scientific Research 6P06S04121 project.
    Źródło:
    Archives of Hydro-Engineering and Environmental Mechanics; 2003, 50, 1; 37-57
    1231-3726
    Pojawia się w:
    Archives of Hydro-Engineering and Environmental Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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:
    Two-dimensional shallow water model for rapidly and gradually varied flow
    Autorzy:
    Szydłowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/241012.pdf
    Data publikacji:
    2001
    Wydawca:
    Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
    Tematy:
    Two-dimensional shallow water model
    rapidly varied flow
    gradually varied flow
    shallow water equations
    eddy viscosity terms
    Opis:
    The numerical solution of full shallow water equation (SWE) including the eddy viscosity terms is presented. In the first part of the paper the solution of the homogeneous part of SWE for discontinuous, rapidly varied flow is reported. The method presented here is based on Roe idea of numerical fluxes of mass and momentum. The numerical solution of SWE on unstructured, triangular mesh is reported and the influence of geometry approximation is examined. The imposing of the boundary condition on a triangular numerical mesh is described in detail. The consistent with finite volume method (FVM) approximation of the viscous part of SWE is presented. The procedure similar to the finite element method (FEM) is used to calculate the function derivatives inside the finite volumes. The specific difficulties of source terms numerical integration are studied and some methods to avoid these problems are presented. To integrate the bottom friction term the splitting technique is implemented. The computed results are compared to analytical solution of Saint-Venant equations, experimental data and results available in the literature. Good agreement between these results is observed.
    Źródło:
    Archives of Hydro-Engineering and Environmental Mechanics; 2001, 48, 1; 35-61
    1231-3726
    Pojawia się w:
    Archives of Hydro-Engineering and Environmental Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical simulation of extreme flooding in a built-up area
    Autorzy:
    Szydłowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/241362.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
    Tematy:
    flash flooding
    urban area
    mathematical modelling
    shallow water equations
    finite volume method
    numerical simulation
    Opis:
    Two numerical simulations of extreme (flash) flood propagation in an urban area are presented. The simulations are performed to recognize some specific features of flow in a built-up area. As the mathematical model of free surface unsteady water flow the shallow water equations are assumed. In order to solve the equations, a numerical scheme based on finite volume method is applied. For approximation of mass and momentum fluxes the Roe method is used. The calculations are examined against the experimental data. The measured variations of water depth at some control points of flooded area are available due to physical modelling. The experiments of model city flooding events were carried out at the hydraulic laboratory of ENEL-CESI in Milan (Italy) in a framework of EC IMPACT project. The aim of these experiments was to simulate a flood in the area where a building group representing a simplified city configuration was introduced.
    Źródło:
    Archives of Hydro-Engineering and Environmental Mechanics; 2005, 52, 4; 321-333
    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
    Tytuł:
    Kinetic-induced moment systems for the Saint-Venant equations
    Autorzy:
    Gil Montoya, D. C.
    Struckmeier, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/1933941.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Gdańska
    Tematy:
    Saint-Venant equations
    shallow water equations
    Boltzmann equation
    hyperbolic conservation laws
    kinetic models
    kinetic representations
    relaxion systems
    shock waves
    rarefaction waves
    Opis:
    Based on the relation between kinetic Boltzmann-like transport equations and nonlinear hyperbolic conservation laws, we derive kinetic-induced moment systems for the spatially one-dimensional shallow water equations (the Saint-Venant equations). Using Chapman-Enskog-like asymptotic expansion techniques in terms of the relaxation parameter of the kinetic equation, the resulting moment systems are asymptotically closed without the need for an additional closure relation. Moreover, the new second order moment equation for the (asymptotically) third order system may act as a monitoring function to detect shock and rarefaction waves, which we confirm by a number of numerical experiments.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2013, 17, 1-2; 63-90
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finite-volume solvers for a multilayer Saint-Venant system
    Autorzy:
    Audusse, E.
    Bristeau, M. O.
    Powiązania:
    https://bibliotekanauki.pl/articles/929697.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Saint-Venanta
    równanie płytkiej wody
    wolumen skończony
    problem Riemanna
    model wielowarstwowy
    Saint-Venant system
    shallow water equations
    finite volumes
    kinetic solver
    approximate Riemann solvers
    multilayer model
    Opis:
    We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 311-320
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An Approximate solution to the Boussinesq type equations describing periodic waves
    Autorzy:
    Szmidt, J. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/240984.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
    Tematy:
    Boussinesq type equations
    shallow water
    Opis:
    The paper concerns the non-linear problem of description of shallow-water waves of finite amplitude. The description is based on the conservation-law formulation, which seems to be particularly convenient in constructing an approximate solution of the problem considered. The analysis is confined to the one-dimensional case of waves propagating in water of constant depth. In the model considered, vertical acceleration of the fluid is taken into account, and thus, the fundamental equations of the problem are similar to those given by Boussinesq (Abbott 1979). The equations differ from those frequently used in shallow-water hydrodynamics which are based on the assumption of hydrostatic pressure. An approximate solution of the problem is constructed by means of a perturbation scheme with the third order expansion of the equations with respect to a small parameter. It is demonstrated that the solution procedure may be successfully applied only within a certain range of the two ratios defining wave height to water depth and the depth to wave length, respectively.
    Źródło:
    Archives of Hydro-Engineering and Environmental Mechanics; 2003, 50, 3; 269-285
    1231-3726
    Pojawia się w:
    Archives of Hydro-Engineering and Environmental Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A finite element method for extended KdV equations
    Autorzy:
    Karczewska, A.
    Rozmej, P.
    Szczeciński, M.
    Boguniewicz, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/330630.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    shallow water wave problem
    nonlinear equations
    second order KdV equations
    finite element method
    Petrov–Galerkin method
    Opis:
    The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2016, 26, 3; 555-567
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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