Technical Papers
Jun 15, 2012

SPH Modeling of Shallow Flow with Open Boundaries for Practical Flood Simulation

Publication: Journal of Hydraulic Engineering
Volume 138, Issue 6

Abstract

A smoothed particle hydrodynamics (SPH) numerical model for shallow water equations (SWEs) is presented for simulating flood inundation owing to rapidly varying flow, such as dam breaks, tsunamis, and levee breaches. Important theoretical and numerical developments have recently been made, and the model in this paper incorporates these developments and implements open boundary conditions, resulting in a general, accurate computational tool suitable for practical application. The method is attractive for flood simulation over large domains in which the extent of inundation is unknown because computation is carried out only in wet areas and is dynamically adaptive. The open boundary algorithm is very general, on the basis of a simplified version of the characteristics method, handling both supercritical and subcritical inflow and outflow. This is tested against reference solutions for flows over a hump involving shocks. The model is then applied to two very different flood inundations resulting from the Okushiri tsunami in Japan and from a hypothetical dyke breach at Thamesmead in the United Kingdom. The SPH-SWE model compares well with established commercial and state-of-the-art finite-volume codes.

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Acknowledgments

The authors want to acknowledge the anonymous reviewers who provided useful comments and suggestions, which improved the quality of the paper. This work was funded by a Research Councils UK (RCUK) Research Fellowship and contributes to the Flood Risk Management Research Consortium (FRMRC). The FRMRC is supported by grant EP/F020511/1 from the Engineering and Physical Sciences Research Council, in partnership with the DEFRA/EA Joint Research Programme on Flood and Coastal Defence, UKWIR, OPW (Ireland), and the Rivers Agency (Northern Ireland).

References

Ata, R., and Soulaïmani, A. (2004). “A stabilized SPH method for inviscid shallow water flows.” Int. J. Numer. Methods FluidsIJNFDW, 47(2), 139–159.
Aureli, F., Maranzoni, A., Mignosa, P., and Ziveri, C. (2008). “A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography.” Adv. Water Resour.AWREDI, 31(7), 962–974.
Bonet, J., and Lok, T.-S. L. (1999). “Variational and momentum preservation aspects of smooth particle hydrodynamic formulations.” Comput. Methods Appl. Mech. Eng.CMMECC, 180(1–2), 97–115.
de Leffe, M., Le Touzé, D., and Alessandrini, B. (2010). “SPH modeling of shallow-water coastal flows.” J. Hydraul. Res.JHYRAF, 48(sup1), 118–125.
Delis, A. I., Kazolea, M., and Kampanis, N. A. (2008). “A robust high-resolution finite volume scheme for the simulation of long waves over complex domains.” Int. J. Numer. Methods FluidsIJNFDW, 56(4), 419–452.
Feldman, J., and Bonet, J. (2007). “Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems.” Int. J. Numer. Methods Eng.IJNMBH, 72(3), 295–324.
Fujihara, M., and Borthwick, A. G. L. (2000). “Godunov-type solution of curvilinear shallow-water equations.” J. Hydraul. Eng.JHEND8, 126(11), 827–836.
Lastiwka, M., Basa, M., and Quinlan, N. J. (2009). “Permeable and non-reflecting boundary conditions in SPH.” Int. J. Numer. Methods FluidsIJNFDW, 61(7), 709–724.
LeVeque, R. J., and George, D. L. (2007). “High-resolution finite volume methods for the shallow water equations with bathymetry and dry states.” Advanced numerical models for simulating tsunami waves and runup: Advances in coastal and ocean engineering, Yeh, H., Lui, P. and Synolakis, C., eds., World Scientific, Singapore.
Liang, Q., Du, G., Hall, J. W., and Borthwick, A. G. L. (2008). “Flood inundation modeling with an adaptive quadtree grid shallow water equation solver.” J. Hydraul. Eng., 134(11), 1603–1610.JHEND8
Monaghan, J. J. (2005). “Smoothed particle hydrodynamics.” Rep. Prog. Phys.RPPHAG, 68(8), 1703–1759.
Rodriguez-Paz, M., and Bonet, J. (2005). “A corrected smooth particle hydrodynamics formulation of the shallow-water equations.” Comput. Struct.CMSTCJ, 83(17–18), 1396–1410.
Rogers, B. D., Borthwick, A. G. L., and Taylor, P. H. (2003). “Mathematical balancing of flux gradient and source terms prior to using Roe’s approximate Riemann solver.” J. Comput. Phys., 192(2), 422–451.JCTPAH
Shepard, D. (1968). “A two-dimensional interpolation function for irregularly-spaced data.” Proc., ACM National Conf., Brandon/Systems, Princeton, NJ.
Vacondio, R., Rogers, B. D., and Stansby, P. K. (2011a). “Smoothed particle hydrodynamics: Approximate zero-consistent 2-D boundary conditions and still shallow-water tests.” Int. J. Numer. Methods FluidsIJNFDW, (Apr. 12, 2011).
Vacondio, R., Rogers, B. D., and Stansby, P. K. (2011b). “Accurate particle splitting for smoothed particle hydrodynamics in shallow water with shock capturing.” Int. J. Numer. Methods FluidsIJNFDW, (Jul. 25, 2011).
Vacondio, R., Rogers, B. D., Stansby, P. K., Mignosa, P., and Feldman, J. (2011c). “A dynamic particle coalescing and splitting scheme for SPH.” Proc., 6th Int. SPHERIC Workshop, Schriftenreihe Shiffbau, Hamburg, Germany, 93–100.
Valdez-Balderas, D., Dominguez, J. M., Crespo, A. J. C., and Rogers, B. D. (2011). “Developing massively parallel SPH simulations on multi-GPU cluster.” Proc., 6th Int. SPHERIC Workshop, Schriftenreihe Shiffbau, Hamburg, Germany, 340–347.
Valiani, A., and Begnudelli, L. (2006). “Divergence form for bed slope source term in shallow water equations.” J. Hydraul. Eng.JHEND8, 132(7), 652–665.
Vila, J. P. (1999). “On particle weighted methods and smoothed particle hydrodynamics.” Math. Models Methods Appl. Sci., 9(2), 161–209.MMMSEU

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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 138Issue 6June 2012
Pages: 530 - 541

History

Received: Nov 11, 2010
Accepted: Dec 6, 2011
Published online: Dec 8, 2011
Published in print: Jun 1, 2012
Published ahead of production: Jun 15, 2012

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Authors

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R. Vacondio [email protected]
Dept. of Civil and Environmental Engineering and Architecture (DICATeA), Univ. of Parma, Viale G. P. Usberti 181/A, 43100 Parma, Italy (corresponding author). E-mail: [email protected]
B. D. Rogers [email protected]
School of Mechanical, Aerospace, and Civil Engineering, Univ. of Manchester, Manchester, U.K. E-mail: [email protected]
P. K. Stansby [email protected]
School of Mechanical, Aerospace, and Civil Engineering, Univ. of Manchester, Manchester, U.K. E-mail: [email protected]
Dept. of Civil and Environmental Engineering and Architecture (DICATeA), Univ. of Parma, Viale G. P. Usberti 181/A, 43100 Parma, Italy. E-mail: [email protected]

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