Solution of the Dike-break Problem Using Finite Volume Method and Splitting Technique

• Autorzy: Gąsiorowski D.
• Konferencja: Application of Computer Methods in Free-Surface and Pressurized Flow Modeling
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

finite volume method; shallow water equations; approximate Riemann solver; dambreak; dike-break

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2011
• Tom: Vol. 15, No 3-4
• Strony: 251--270
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Gąsiorowski D.

• Gdańsk University of Technology, Faculty of Civil Environmental Engineering,

Bibliografia

• [1] Cunge J A, Holly Jr F M and Yerwey A 1980 Practical Aspects of Compututional RWKT Hydraulic.fi, Pitman, London
• [2] Tan Weiyan 1992 Shallow Water Hydrodynamics, Elsevier. Amsterdam
• [3] Szymkiewicz R 2010 Numerical Modeling in Open Chanel Hydraulics, Springer
• [4] Toro E F 1997 Rie.mann Solvers and Numerical Me.thods for Fluid Dynamics, Springer-Verlag, Berlin
• [5] LeVeque R J 2002 Finite Yolurne Methods for Hyperbolic Problems, Cambridge University Press
• [6] Glaister P 1988 J. Hydraul Re.s. 26 (3) 293
• [7] Suaders B F 2001 J. Hydraul. Res. 39 (3)
• [8] Nujic M 1995 J. Hydraul. Res. 33 (1) 101
• [9] Mingham C G and Causon D M 1998 J. Hydraul. Engng 124 (6) 005
• [10] Szydłowski M 2001 Arch. Hydro-Engng Enmron. Mech. XLVIII (1) 35
• [11] Aureli F and Mignosa P 2002 Rapidly Yarying Flows Due. to Levee-Breaking, River Flow 2002. Proc. First Int. Conf. on Flumal Hydraulics, Louvain La Neuvc, Belgium (Bousmar D a.nd Zech Y, Eds.)
• [12] Liang Q, Borthwick A G and Stelling G 2004 Int. J. Num. Meth. in Fluids 46 127
• [13] R.oger S, Dewals B J. Erpicum S. Schwanenberg D, Schuttrumpf H, Kóngeter .J and Piroton M 2009 J. Hydraul. Res. 47 (3) 349
• [14] LcYeąue R J 1997 J. Comput. Phys. 131 327
• [15] Bale D S, LeYeąue R J, Mitrau S and Rossmanith 3 A 2002 SIAM, J. Sci. Comput. 24 (3) 995
• [16] Szymkiewicz R 1993 J. Hydraul. Engng 119 (10) 1118
• [17] Roe P L 1981 J. Comput. Phys. 43 357
• [18] Fletcher P S 1991 Computational Technigues for Fluid Medianics, Spriuger Yeiiag, Berlin
• [19] Bermudez A and Vazquez M E 1994 Compule.ru and Fluids 23 1049
• [20] Garcia-Navarro P and Vazquez-Cendon M E 2000 Computers and Fluids 29 951
• [21] Stoker J J 1957 Water Wanes. Interscience Publishers
• [22] Wu C, Huaug G and Zheng Y 1999 J. Hydraul. Engng 125 (11) 1210
• [23] Fennema R ,1 a.nd Chaudhry M H 1990 J. Hydraul. Engng 116 (8) 1013
• [24] Szydłowski M 2007 Moddlmg of Flood Waves in Urban Arcas. Gdańsk University of Technology (in Polish)