Current Science

Open Access Open Access  Restricted Access Subscription Access

Simulation of One Dimensional Open Channel Flows Using the SPH Model


Affiliations
1 Department of Civil Engineering, Malaviya National Institute of Technology Jaipur, Jaipur 302 017, India
2 Discipline of Civil Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382 355, India
 

In this study, shallow water equations with source terms were numerically solved using the smoothed particle hydrodynamics (SPH) method. The proposed model can incorporate the inflow and outflow boundaries. In addition, bed discontinuity was modelled using the fluid particles without any extra bed particles. Artificial viscosity to smoothen the numerical oscillations in the water surface profile was considered. The sensitivity and convergence analyses were used to determine the optimal model parameters. Seven different kinds of open channel flow in prismatic channels were simulated to demonstrate the model’s capabilities. The numerical accuracy was quantified in terms of L2 error norm. Comparison with earlier results shows that the SPH model can be used to compute steady and unsteady open channel flows with or without bed discontinuity.

Keywords

Hydraulics, Open Channel Flow, Shallow Water Equations, Smoothened Particle Hydrodynamics.
User
Notifications
Font Size

  • Chaudhry, M. H., Open Channel Flow, Springer, New York, USA, 2008, 2nd edn.

  • Cunge, J. A., Holly, F. M. and Verwey, A., Practical Aspects of Computational River Hydraulics, Pitman Advanced Publishing Program, London, UK, 1980, p. 420.

  • Liu, G. R. and Liu, M. B., Smoothed Particle Hydrodynamics: AMeshfree Particle Method, World Scientific Publishing, Singapore, 2003.

  • Wang, Z. and Shen, H. T., Lagrangian simulation of one-dimensional dam-break flow. J. Hydraul. Eng., 1999, 125(11), 1217–1220.

  • Monaghan, J. J., Smoothed particle hydrodynamics. Rep. Progress Phys., 2005, 68(3), 1703–1759.

  • Monaghan, J. J., Smoothed particle hydrodynamics. Ann. Rev. Fluid Mech., 2012, 44, 323–346.

  • Gomez-Gesteira, M., Rogers, B. D., Dalrymple, R. A. and Crespo, A. J. C., State of the art of classical SPH for free-surface flows. J. Hydraul. Res., 2010, 48(1), 6–27.

  • Violeau, D. and Rogers, B. D., Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future. J. Hydraul. Res., 2016, 54(1), 1–26.

  • Monaghan, J. J., Simulating free surface flows with SPH. J. Comput. Phys., 1994, 110(2), 399–406.

  • Swegle, J. W., Hicks, D. L. and Attaway, S. W., Smoothed particle hydrodynamics stability analysis. J. Comput. Phys., 1995, 116(1), 123–134.

  • Morris, J. P., Fox, P. J. and Zhu, Y., Modelling low Reynolds number incompressible flows using SPH. J. Comput. Phys., 1997, 136(1), 214–226.

  • Bonet, J. and Lok, T. S. L., Variational and momentum preservation aspects of smoothed particle hydrodynamics formulations. Comput. Methods Appl. Mech. Eng., 1999, 180(1–2), 97–115.

  • Cummins, S. J. and Rudman, M. J., An SPH projection method. J. Comput. Phys., 1999, 152(2), 584–607.

  • Inutsuka, S. I., Reformulation of smoothed particle hydrodynamics with Riemann solver. J. Comput. Phys., 2002, 179(1), 238–267.

  • Cha, S. H. and Whitworth, A. P., Implementations and tests of Gudunov-type particle hydrodynamics. Mon. Notice R. Astro. Soc., 2003, 340, 73–90.

  • Rodriguez-Paz, M. and Bonet, J., A corrected smooth particle hydrodynamics formulation of the shallow-water equations. Comput. Struct., 2005, 83(17–18), 1396–1410.

  • Hu, X. Y. and Adams, N. A., A multi-phase SPH method for macroscopic and mesoscopic flows. J. Comput. Phys., 2006, 213(2), 844–861.

  • Grenier, N., Antuono, M., Colagrossi, A., Le-Touze, D. and Alessandrini, B., A Hamiltonian interface SPH formulation for multi-fluid and free surface flows. J. Comput. Phys., 2009, 228(22), 8380–8393.

  • De-Leffe, M., Le-Touze, D. and Alessandrini, B., SPH modeling of shallow-water coastal flows. J. Hydraul. Res., 2010, 48(1), 118–125.

  • Vila, J. P., On particle weighted methods and smoothed particle hydrodynamics. Math. Models Methods Appl. Sci., 1999, 9(2), 161–209.

  • Chang, T. J., Kao, H. M., Chang, K. H. and Hsu, M. H., Numerical simulation of shallow-water dam break flows in open channels using smoothed particle hydrodynamics. J. Hydrol., 2011, 408(1–2), 78–90.

  • Kao, H. M. and Chang, T. J., Numerical modeling of dam break-induced flood and inundation using smoothed particle hydrodynamics. J. Hydrol., 2012, 448, 232–244.

  • Vacondio, R., Rogers, B. D. and Stansby, P. K., Accurate particle splitting for smoothed particle hydrodynamics in shallow water with shock capturing. Int. J. Numer. Methods Fluids, 2012, 69(8), 1377–1410.

  • Vacondio, R., Rogers, B. D., Stansby, P. K. and Mignosa, P., SPH modeling of shallow flow with open boundaries for practical flood simulation. J. Hydraul. Eng., 2012, 138(6), 530–541.

  • Meister, M., Burger, G. and Rauch, W., On the Reynolds number sensitivity of smoothed particle hydrodynamics. J. Hydraul. Res., 2014, 52(6), 824–835.

  • Sun, P. N., Colagrossi, A., Marrone, S. and Zhang, A. M., The δ plus-SPH model: simple procedures for a further improvement of the SPH scheme. Comput. Methods Appl. Mech. Eng., 2017, 315, 25–49.

  • Chang, K. H., Sheu, T. W. H. and Chang, T. J., A 1D–2D coupled SPH–SWE model applied to open channel flow simulations in complicated geometries. Adv. Water Resour., 2018, 115, 185–197.

  • Gu, S., Bo, F., Luo, M., Kazemi, E., Zhang, Y. and Wei, J., SPH simulation of hydraulic jump on corrugated riverbeds. Appl. Sci., 2019, 9(3), 436.

  • Hsu, T. W., Liang, S. J. and Wu, N. J., Application of meshless SWE model to moving wet/dry front problems. Eng. Comput., 2019, 35(1), 291–303.

  • Hsu, T. W., Liang, S. J. and Wu, N. J., A 2D SWE meshless model with fictitious water level at dry nodes. J. Hydraul. Res., 2021, 59(6), 917–931.

  • Chang, K. H., Chang, T. J. and Garcia, M. H., A well-balanced and positivity-preserving SPH method for shallow water flows in open channels. J. Hydraul. Res., 2021, 59(6), 903–916.

  • Vacondio, R., Rogers, B. D., Stansby, P. K. and Mignosa, P., A correction for balancing discontinuous bed slopes in two-dimensional smoothed particle hydrodynamics shallow water modeling. Int. J. Numer. Methods Fluids, 2013, 71(7), 850–872.

  • Ferrari, A., Dumbser, M., Toro, E. F. and Armanini, A., A new 3D parallel SPH scheme for free surface flows. Comput. Fluids, 2009, 38(6), 1203–1217.

  • Federico, Marrone, S., Colagrossi, A., Aristodemo, F. and Antuono, M., Simulating 2D open-channel flows through an SPH model. Eur. J. Mech. B/Fluids, 2012, 34, 35–46.

  • Stoker, J. J., Water Waves: Mathematical Theory with Applications, Wiley-Interscience, Singapore, 1957.

  • LaRocque, L. A., Imran, J. and Chaudhry, M. H., Experimental and numerical investigations of two dimensional dam break flows. J. Hydraul. Eng., 2013, 139(6), 569–579.

  • Ritter, A., The propagation of water waves. Ver Deut. Ing.-Z., 1982, 36(33), 947–954.

  • Chanson, H., Analytical solutions of laminar and turbulent dam break wave. In Proceedings of the International Conference on Fluvial Hydraulics River Flow, Taylor and Francis, London, 2006, pp. 465–474.

  • Aureli, F., Maranzoni, A., Mignosa, P. and Ziveri C., A weighted surface–depth gradient method for the numerical integration of the 2D shallow water equations with topography. Adv. Water Resour., 2008, 31(7), 962–974.

  • Gharangik, A. M. and Chaudhry, M. H., Numerical simulation of hydraulic jump. J. Hydraul. Eng., 1991, 117(9), 1195–1211.

  • Ye, J. and McCorquodale, J. A., Depth averaged hydrodynamic model in curvilinear collocated grid. J. Hydraul. Eng., 1997, 123(5), 380–388.


Abstract Views: 230

PDF Views: 100




  • Simulation of One Dimensional Open Channel Flows Using the SPH Model

Abstract Views: 230  |  PDF Views: 100

Authors

Manoj Kumar Diwakar
Department of Civil Engineering, Malaviya National Institute of Technology Jaipur, Jaipur 302 017, India
Pranab Kumar Mohapatra
Discipline of Civil Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382 355, India

Abstract


In this study, shallow water equations with source terms were numerically solved using the smoothed particle hydrodynamics (SPH) method. The proposed model can incorporate the inflow and outflow boundaries. In addition, bed discontinuity was modelled using the fluid particles without any extra bed particles. Artificial viscosity to smoothen the numerical oscillations in the water surface profile was considered. The sensitivity and convergence analyses were used to determine the optimal model parameters. Seven different kinds of open channel flow in prismatic channels were simulated to demonstrate the model’s capabilities. The numerical accuracy was quantified in terms of L2 error norm. Comparison with earlier results shows that the SPH model can be used to compute steady and unsteady open channel flows with or without bed discontinuity.

Keywords


Hydraulics, Open Channel Flow, Shallow Water Equations, Smoothened Particle Hydrodynamics.

References





DOI: https://doi.org/10.18520/cs%2Fv124%2Fi12%2F1422-1430