Diagonal Cartesian Method for the Numerical Simulation of Flow and Suspended Sediment Transport over Complex Boundaries
Publication: Journal of Hydraulic Engineering
Volume 132, Issue 11
Abstract
There is increasing demand for simulation tools of flow and suspended sediment transport over complex boundaries in hydraulic engineering. The diagonal Cartesian method, which approximates complex boundaries using both Cartesian grid lines and diagonal lines segments, is presented in the paper to simulate the complex boundaries of two-dimensional shallow-water turbulence equations and nonequilibrium suspended sediment transport equation. The method, which utilizes cell-centered nodes on a nonstaggered grid, uses boundary velocity information at the wall boundary to avoid the specification of water level. An enlarged finite-difference method is introduced for momentum and suspended sediment equations on the complex boundary. This paper describes an application of the diagonal Cartesian method to calculate the tidal current and suspended sediment concentration of Quanzhou Bay in the Fujian province of China. The results show that the method predicts the flow and suspended sediment concentration well, and the calculations agree well with the measurement.
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Acknowledgments
The research work is supported by the National Science Foundation of China, Grant No. 50325929, Beijing, China.
References
Bowden, K. F., Fairbairn, L. A., and Hughes, P. (1959). “The distribution of shear stresses in tidal current.” Geophys. J. R. Astron. Soc., 2, 288–305.
Bradford, S. F., and Sanders, B. F. (2002). “Finite-volume model for shallow-water flooding of arbitrary topography.” J. Hydraul. Eng., 128(3), 289–298.
Carlson, K. D., Tien, H. C., and Chen, C. J. (1993). “Finite analytic numerical simulation of fluid dynamics problems involving irregular geometries.” Proc., Refined Flow Modeling and Turbulence Measurements, International Association for Hydraulic Research, Delft, The Netherlands, 199–206.
Chen, C. J. (1986). “Finite analytic method.” Handbook of numerical heat transfer, Wiley, New York, 723–746.
Chen, C. J., Tien, H. C., Carlson, K. D., and Bernatz, R. A. (1993). “Finite analytic method for 2D and 3D flows with complex geometry.” Proc., Refined Flow Modeling and Turbulence Measurements, Paris, 161–174.
Fang, H. W., Chen, C. J., and Lin, W. L. (2000). “Three-dimensional diagonal Cartesian method for incompressible flows involving complex boundaries.” Numer. Heat Transfer, Part B, 38(3), 37–57.
Fang, H. W., and Wang, G. Q. (2000). “Three-dimensional mathematical model of suspended sediment transport.” J. Hydraul. Eng., 126(8), 578–592.
Karpik, S. R., and Crockett, S. R. (1997). “Semi-Lagrangian algorithm for two-dimensional advection-diffusion equation on curvilinear meshes.” J. Hydraul. Eng., 123(5), 389–401.
Lapidus, L., and Pinder, G. F. (1982). Numerical solution of partial differential equations in science and engineering, Springer-Verlag, New York.
Lin, W. L., Carlson, K. D., and Chen, C. J. (1998). “Diagonal Cartesian method for numerical simulation of incompressible flow over complex boundary.” Numer. Heat Transfer, Part A, 33(5), 181–213.
Lin, W. L., Carlson, K. D., and Chen, C. J. (1999). “Numerical modeling of conjugate heat transfer on complex geometries with diagonal Cartesian method. Part I: Methods.” J. of Heat Transfer-transactions, 121(2), 253–260.
Miles, G. V. (1981). Sediment transport models for estuaries, Hydraulic Research Station, Wallingford, U.K.
Nagata, N., Hosoda, T., and Muramoto, Y. (2000). “Numerical analysis of river channel processes with bank erosion.” J. Hydraul. Eng., 126(4), 243–252.
Nakatsuji, K., Sueyoshi, T., and Muraika, K. (1993). “Numerical experiments of residual circulation and its formulation mechanism in tidal estuary.” Proc., Refined Flow Modeling and Turbulence Measurements, International Association for Hydraulic Research, Delft, The Netherlands, 695–702.
Ni, J. R., Zhang, H. W., Xue, A., Wieprecht, S., and Borthwick, A. G. L. (2004). “Modeling of hyperconcentrated sediment-laden floods in lower Yellow River.” J. Hydraul. Eng., 130(10), 1025–1032.
Rodi, W. (1993). Turbulence models and their applications in hydraulics—A state of the art review, 3rd Ed., Balkema, Rotterdam, The Netherlands.
Schwanenberg, D., and Harms, M. (2004). “Discontinuous Galerkinfinite-element method for transcritical two-dimensional shallow water flows.” J. Hydraul. Eng., 130(5), 412–421.
Thompson, F. C., Thames, J. F., and Mastin, C. W. (1974). “Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies.” J. Comput. Phys., 15, 299–310.
Zarrati, A. R., Tamai, N., and Jin, V. C. (2005). “Mathematical modeling of meandering channels with a generalized depth averaged model.” J. Hydraul. Eng., 131(6), 467–475.
Zhang, R. J., and Xie, J. H. (1993). Sedimentation research in China—Systematic sections, China Water and Power Press, Beijing, China.
Zhou, J. G., Causon, D. M., Mingham, C. G., and Ingram, D. M. (2004). “Numerical prediction of dam-break flows in general geometries with complex bed topography.” J. Hydraul. Eng., 130(4), 332–340.
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Information
Published In
Journal of Hydraulic Engineering
Volume 132 • Issue 11 • November 2006
Pages: 1195 - 1205
Copyright
© 2006 ASCE.
History
Received: Oct 5, 2004
Accepted: Nov 8, 2005
Published online: Nov 1, 2006
Published in print: Nov 2006
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