Comparison of Finite Volume Method and Smoothed Particle Hydrodynamic in Modeling of Flow over Sharp-Crested Weir

Document Type : Research Paper

Authors

• Ali Mahdavi
• Hossein Khorshidi

Abstract

This study presents a new hybrid algorithm for treating solid wall boundaries in the context of smoothed particle hydrodynamics (SPH) model. In this way, the basic concept is to fill an impervious region with some layers of dummy particles for improving the solution accuracy, and a single layer of repulsive particles to impose a no-penetration condition along the solid-fluid interface. The later consists of a new repulsion mechanism that, unlike the well-known Lennard-Jones model, induces no pressure oscillation close to the wall region. This hybrid boundary treatment technique is implemented in conjunction with a parameter-free smoothed particle hydrodynamics scheme to provide a Lagrangian solver for two dimensional Navier Stokes equations. The accuracy of the model is verified by recourse to challenging a numerical test defined for a free falling water jet from a sharp crested weir. The computed nappe profiles are compared with those of a finite volume method. Satisfactory agreement is found between all these results.  

Keywords

• SPH
• Solid boundary condition
• free surface flow
• Sharp-crested weir
• Finite Volume Method

20.1001.1.20086377.1396.10.35.7.9

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References

 

1)        Vischer, D.L., and Hager, W.H. 1998. Dam Hydraulics, Wiley, UK.

2)        Ferrari, A. 2010. SPH simulation of free surface flow over a sharp-crested weir. Advances in Water Resources, 33: 270-276.

3)        Gingold, R.A., and Monaghan, J.J. 1977. Smoothed particle hydrodynamics-theory and application to nonspherical stars. Monthly Notices of the Royal Astronomical Society, 181: 375-389.

4)        Lucy, L.B. 1977. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 82:  1013-1024.

5)        Libersky, L.D., Petschek, A.G., Carney, T.C., Hipp, J.R. and Allahadi, F.A. 1993. High strain Lagrangian hydrodynamics: A three-dimensional SPH code for dynamic material response. Journal of Computational Physics, 109:   67-75.

6)        Monaghan, J.J. 1994. Simulating free surface flows with SPH. Journal of Computational Physics, 110: 399-406.

7)        Gomez-Gesteira, M. and Dalrymple, R.A. 2004. Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure. Journal of Waterway, Port, Coastal, and Ocean Engineering, 130: 63-69.

8)        Liu, M.B., and Liu, G.R. 2010. Smoothed particle hydrodynamics (SPH): An overview and recent developments. Archives of Computational Methods in Engineering, 17: 25-76.

9)        Monaghan, J.J. 2005. Smoothed particle hydrodynamics. Reports on Progress in Physics, 68: 1703-1759.

10)    Monaghan, J.J. 2012. Smoothed particle hydrodynamics and its diverse applications. Annual Review of Fluid Mechanics, 44: 323-346.

11)    Souto-Iglesias, A., Perez-Rojas, L. and Zamora Rodriguez, R. 2004. Simulation of anti-roll tanks and sloshing type problems with smoothed particle hydrodynamics. Ocean Engineering, 31:   1169-1192.

12)    Souto-Iglesias, A., Delorme, L., Perez-Rojas, L. and Abril-Perez, S. 2006. Liquid moment amplitude assessment in sloshing type problems with smooth particle hydrodynamics. Ocean Engineering, 33:   1462-1484.

13)    Randles, P.W., and Libersky, L.D. 1996. Smoothed particle hydrodynamics: Some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering, 139:   375-408.

14)    Colagrossi, A. and Landrini, M. 2003. Numerical simulation of interfacial flows by smoothed particle hydrodynamics. Journal of Computational Physics, 191: 448-475.

15)    Crespo, A.J.C., Gomez-Gesteira, M. and Dalrymple, R.A. 2007. 3D SPH simulation of large waves mitigation with a dike. Journal of Hydraulic Research, 45:   631-642.

16)    Goomez-Gesteira, M., Rogers, B.D., Dalrymple, R.A. and Crespo, A.J. 2010. State-of-the-art of classical SPH for free-surface flows. Journal of Hydraulic Research, 48: 6-27.

17)    Liu, G.R., and Liu, M.B., 2003. Smoothed Particle Hydrodynamics: A Mesh free Particle Method, World Scientic, Singapore.

18)    Rogers, B.D. and Dalrymple, R.A. 2008. SPH Modeling of tsunami waves. In Advanced Numerical Models for Tsunami Waves and Runup, World Scientic, Singapore.

19)    Shao, J.R., Li, H.Q., Liu, G.R. and Liu, M.B. 2012. An improved SPH method for modeling liquid sloshing dynamics. Computers and Structures, 100:   18-26.

20)    Lo, E.Y.M. and Shao, S.D. 2002. Simulation of near-shore solitary wave mechanics by an incompressible SPH method. Applied Ocean Research, 24:   275-286.

21)    Shao, S.D. and Lo, E.Y.M. 2003. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Advances in Water Resources, 26: 787-800.

22)    Mingham, C. G., and D. M. Causon 1998. High-resolution finite-volume method for shallow water flows. Journal of Hydraulic Engineering 124: 605-614.

23)    Qu, J., A. S. Ramamurthy, R. Tadayon, and Z. Chen. 2009. Numerical simulation of sharp-crested weir flows. Canadian Journal of Civil Engineering 36: 1530-1534.

24)    Bhajantri, M. R., T. I. Eldho, and P. B. Deolalikar. 2006. Hydrodynamic modelling of flow over a spillway using a two-dimensional finite volume-based numerical model. Sadhana 31: 743-754.

25)    Dumbser, Michael. 2011. A simple two-phase method for the simulation of complex free surface flows. Computer Methods in Applied Mechanics and Engineering 200: 1204-1219.

26)    Versteeg, H. K. and Malalasekera, W. 1995. An introduction to computational fluid dynamics: The finite volume method. Longman house, Burnt Mill Harlow Essex CM20 2JE, England.

27)    Blazek, J. 2001. Computational Fluid Dynamics: Principles and Applications. Alstom Power Ltd., Baden-Daettwil, Switzerland.

28)    Ferrari, A., Dumbser, M., Toro, E.F. and Armanini, A. 2009. A new 3D parallel SPH scheme for free surface flows. Computers and Fluids, 38: 1203-1217.

29)    Toro, E.F. 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics, 3th Edn. Springer, Germany.

30)    Hu, X.Y. and Adams, N.A. 2006. A multi-phase SPH method for macroscopic and mesoscopic flows. Journal of Computational Physics, 213: 844-861.

31)    Adami, S., Hu, X.Y. and Adams, N.A. 2012. A generalized wall boundary condition for smoothed particle hydrodynamics. Journal of Computational Physics, 231: 7057-7075.

32)    Delorme, L., Colagrossi, A., Souto-Iglesias, A., Zamora-Rodriguez, R. and Botia-Vera, E. 2009. A set of canonical problems in sloshing, Part I: Pressure field in forced roll-comparison between experimental results and SPH. Ocean Engineering, 36: 168-178.

33)    Fluent team, Manual and user guide of fluent software, 2005. Fluent Inc. Center Resource Park 10 Cavendish Court Lebanon, NH 03766.