Analysis of floodplain inundation using 2D nonlinear diffusive wave equation solved with splitting technique

Czasopismo : Acta Geophysica
Tytuł artykułu : Analysis of floodplain inundation using 2D nonlinear diffusive wave equation solved with splitting technique

Autorzy :
Nowożyński, K.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, kn@igf.edu.pl,
Ślęzak, K.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, katarzyna.slezak@igf.edu.pl,
Kądziałko-Hofmokl, M.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, magdahof@igf.edu.pl,
Szczepański, J.
Institute of Geological Sciences, University of Wrocław, Wrocław, Poland, jacek.szczepanski@ing.uni.wroc.pl,
Werner, T.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, twerner@igf.edu.pl,
Jeleńska, M.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, bogna@igf.edu.p,
Nejbert, K.
Institute of Geochemistry, Mineralogy and Petrology, Warsaw University, Warszawa, Poland, knejbert@uw.edu.pl,
Shireesha, M.
National Geophysical Research Institute, Council of Scientific and Industrial Research, Hyderabad, India, shireeshageo.m@gmail.com,
Harinarayana, T.
National Geophysical Research Institute, Council of Scientific and Industrial Research, Hyderabad, India, thari54@yahoo.com,
Romashkova, L.
Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, Russia, lina@mitp.ru,
Peresan, A.
The Abdus Salam International Centre for Theoretical Physics, SAND Group, Trieste, Italy,
Arosio, D.
Department of Structural Engineering, Politecnico di Milano, Milan, Italy, diego.arosio@polimi.it,
Longoni, L.
Department of Environmental, Hydraulic, Infrastructures and Surveying Engineering, Politecnico di Milano, Milan, Italy, laura.longoni@polimi.it,
Papini, M.
Department of Environmental, Hydraulic, Infrastructures and Surveying Engineering, Politecnico di Milano, Milan, Italy, monica.papini@polimi.it,
Zanzi, L.
Department of Structural Engineering, Politecnico di Milano, Milan, Italy, luigi.zanzi@polimi.it,
Kostecki, A.
Oil and Gas Institute, Kraków, Poland, kostecki@inig.pl,
Półchłopek, A.
Oil and Gas Institute, Kraków, Poland, polchlopek@inig.pl,
Abbaszadeh, M.
Department of Surveying and Geomatics Engineering, Faculty of Civil Engineering, Babol Noushirvani University of Technology, Babol, Iran, m.abbaszadeh@nit.ac.ir,
Sharifi, M.
Department of Surveying and Geomatics Engineering, College of Engineering, University of Tehran, Tehran, Iran, sharifi@ut.ac.ir,
Nikkhoo, M.
Faculty of Geodesy and Geomatics, K.N. Toosi University of Technology, Tehran, Iran, Mehdi_nikkhoo@yahoo.com,
Di Cristo, C.
1Dipartimento di Ingegneria Civile e Meccanica, Università degli Studi di Cassino e del Lazio Meridionale, Cassino, Italy, dicristo@unicas.it,
Iervolino, M.
Dipartimento di Ingegneria Civile, Design, Edilizia e Ambiente, Seconda Università di Napoli, Aversa, Italy, michele.iervolino@unina2.it,
Vacca, A.
Dipartimento di Ingegneria Civile, Design, Edilizia e Ambiente, Seconda Università di Napoli, Aversa, Italy, vacca@unina.it,
Gąsiorowski, D.
Faculty of Civil and Environmental Engineering, Gda ń sk University of Technology, Gdańsk, Poland, gadar@pg.gda.pl,
Abstrakty : In the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring to the procedure of spatial integration leads to a more general algorithm involving a weighting parameter. Time integration is carried out using a two-level difference scheme with the weighting parameter as well. The resulting tri-diagonal systems of nonlinear algebraic equations are solved using the Picard iterative method. For particular sets of the weighting parameters, the proposed method takes the form of a standard finite element method and various schemes of the finite difference method. On the other hand, for the linear version of the governing equation, the proper values of the weighting parameters ensure an approximation of 3rd order. Since the diffusive wave equation can be solved no matter whether the area is dry or wet, the numerical computations can be carried out over entire domain of solution without distinguishing a current position of the shoreline which is obtained as a result of solution.

Słowa kluczowe : unsteady surface flow, nonlinear diffusive wave equation, splitting method, finite element method, finite difference method,
Wydawnictwo : Instytut Geofizyki PAN
Rocznik : 2013
Numer : Vol. 61, no. 3
Strony : 668 – 689
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DOI :
Cytuj : Nowożyński, K. ,Ślęzak, K. ,Kądziałko-Hofmokl, M. ,Szczepański, J. ,Werner, T. ,Jeleńska, M. ,Nejbert, K. ,Shireesha, M. ,Harinarayana, T. ,Romashkova, L. ,Peresan, A. ,Arosio, D. ,Longoni, L. ,Papini, M. ,Zanzi, L. ,Kostecki, A. ,Półchłopek, A. ,Abbaszadeh, M. ,Sharifi, M. ,Nikkhoo, M. ,Di Cristo, C. ,Iervolino, M. ,Vacca, A. ,Gąsiorowski, D. , Analysis of floodplain inundation using 2D nonlinear diffusive wave equation solved with splitting technique. Acta Geophysica Vol. 61, no. 3/2013
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