Research Papers: Fundamental Issues and Canonical Flows

A Modified Smoothed Particle Hydrodynamics Scheme to Model the Stationary and Moving Boundary Problems for Newtonian Fluid Flows

[+] Author and Article Information
Mohammad Sefid

Associate Professor
School of Mechanical Engineering,
Yazd University,
Yazd 89195-741, Iran
e-mail: mhsefid@yazd.ac.ir

Rouhollah Fatehi

Assistant Professor
Department of Mechanical Engineering,
School of Engineering,
Persian Gulf University,
Bushehr 75169, Iran
e-mail: fatehi@pgu.ac.ir

Rahim Shamsoddini

School of Mechanical Engineering,
Yazd University,
Yazd 89195-741, Iran
e-mail: shamsoddini@stu.yazd.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 24, 2013; final manuscript received September 20, 2014; published online October 21, 2014. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 137(3), 031201 (Oct 21, 2014) (9 pages) Paper No: FE-13-1746; doi: 10.1115/1.4028643 History: Received December 24, 2013; Revised September 20, 2014

A robust modified weakly compressible smoothed particle hydrodynamics (WCSPH) method based on a predictive corrective scheme is introduced to model the fluid flows engaged with stationary and moving boundary. In this paper, this model is explained and practically verified in three distinct laminar incompressible flow cases; the first case involves the lid driven cavity flow for two Reynolds numbers 400 and 1000. The second case is a flow generated by a moving block in the initially stationary fluid. The third case is flow around the stationary and transversely oscillating circular cylinder confined in a channel. These results in comparison with the standard benchmarks also confirm the good accuracy of the present solution algorithm.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Lucy, L. B., 1997, “A Numerical Approach to the Testing of the Fission Hypothesis,” Astron. J., 82, pp. 1013–1024. [CrossRef]
Gingold, R. A., and Monaghan, J. J., 1977, “Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars,” Mon. Not. R. Astron. Soc., 181, pp. 375–389. [CrossRef]
Libersky, L., and Petschek, A. G., 1991, “Smooth Particle Hydrodynamics With Strength of Materials,” Lect. Notes Phys., 395, pp. 248–257. [CrossRef]
Monaghan, J. J., and Kocharyan, A., 1995, “SPH Simulation of Multi-Phase Flow,” Comput. Phys. Commun., 87(1), pp. 225–235. [CrossRef]
Muller, M., Schirm, S., and Teschner, M., 2004, “Interactive Blood Simulation for Virtual Surgery Based on Smoothed Particle Hydrodynamics,” Technol. Health Care, 12(1), pp. 25–31. [CrossRef] [PubMed]
Monaghan, J. J., 1994, “Simulating Free Surface Flows With SPH,” J. Comput. Phys., 110(2), pp. 399–406. [CrossRef]
Morris, J. P., 2000, “Simulating Surface Tension With Smoothed Particle Hydrodynamics,” Int. J. Numer. Meth. Fluids, 33(3), pp. 333–353. [CrossRef]
Cummins, S., and Rudman, M., 1999, “An SPH Projection Method,” J. Comput. Phys., 152(1), pp. 584–607. [CrossRef]
Shao, S. D., and Lo, E. Y. M., 2003, “Incompressible SPH Method for Simulating Newtonian and Non-Newtonian Flows With a Free Surface,” Adv. Water Resour., 26(7), pp. 787–800. [CrossRef]
Koshizuka, S., and Oka, Y., 1996, “Moving Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid,” Nucl. Sci. Eng., 123(3), pp. 421–434.
Lee, E. S., Moulinec, C., Xu, R., Laurence, D., and Stansby, P., 2008, “Comparisons of Weakly Compressible and Truly Incompressible Algorithms for the SPH Mesh Free Particle Method,” J. Comput. Phys., 227(18), pp. 8417–8436. [CrossRef]
Bonet, J., and Lok, T. S., 1999, “Variational and Momentum Preservation Aspects of Smooth Particle Hydrodynamic Formulation,” Comput. Methods Appl. Mech. Eng., 180(1–2), pp. 97–115. [CrossRef]
Rodriguez-Paz, M. X., and Bonet, J., 2004, “A Corrected Smooth Particle Hydrodynamics Method for the Simulation of Debris Flows,” Numer. Methods Partial Differ. Equations, 20(1), pp. 140–163. [CrossRef]
Shadloo, M. S., Zainali, A., Yildiz, M., and Suleman, A. R., 2012, “A Robust Weakly Compressible SPH Method and Its Comparison With an Incompressible SPH,” Int. J. Numer. Methods Eng., 89(8), pp. 939–956. [CrossRef]
Fatehi, R., and Manzari, M. T., 2011, “Error Estimation in Smoothed Particle Hydrodynamics and a New Scheme for Second Derivatives,” Comput. Math. Appl., 61(2), pp. 482–498. [CrossRef]
Fatehi, R., and Manzari, M. T., 2011, “A Remedy for Numerical Oscillations in Weakly Compressible Smoothed Particle Hydrodynamics,” Int. J. Numer. Methods Fluids, 67(9), pp. 1100–1114. [CrossRef]
Hu, X. Y., and Adams, N. A., 2007, “An Incompressible Multi-Phase SPH Method,” J. Comput. Phys., 227(1), pp. 264–278. [CrossRef]
Hu, X. Y., and Adams, N. A., 2009, “A Constant-Density Approach for Incompressible Multi-Phase SPH,” J. Comput. Phys., 228(6), pp. 2082–2091. [CrossRef]
Sadek, S. H., and Yildiz, M., 2013, “Modeling Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics,” ASME J. Fluids Eng., 135(5), p. 051103. [CrossRef]
Jiang, T., Ouyang, J., Zhang, L., and Jin-Lian, R., 2012, “The SPH Approach to the Process of Container Filling Based on Non-Linear Constitutive Models,” Acta Mech. Sin., 28(2), pp. 407–418. [CrossRef]
Kajtar, J. B., and Monaghan, J. J., 2012, “On the Swimming of Fish Like Bodies Near Free and Fixed Boundaries,” Eur. J. Mech. B, 33, pp. 1–13. [CrossRef]
Hashemi, M. R., Fatehi, R., and Manzari, M. T., 2012, “A Modified SPH Method for Simulating Motion of Rigid Bodies in Newtonian Fluid Flows,” Int. J. Nonlinear Mech., 47(6), pp. 626–638. [CrossRef]
Hashemi, M. R., Fatehi, R., and Manzari, M. T., 2011, “SPH Simulation of Interacting Solid Bodies Suspended in a Shear Flow of an Oldroyd-B Fluid,” J. Non-Newton. Fluid, 166(21–22), pp. 1239–1252. [CrossRef]
Cohen, R. C. Z., Cleary, P. W., and Mason, B. R., 2012, “Simulations of Dolphin Kick Swimming Using Smoothed Particle Hydrodynamics,” Hum. Mov. Sci., 31(3), pp. 604–619. [CrossRef] [PubMed]
Yang, J., and Stern, F., 2014, “A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows,” ASME J. Fluids Eng., 136(4), p. 040904. [CrossRef]
Raman, S. K., Prakash, K. A., and Vengadesan, S., “Effect of Axis Ratio on Fluid Flow Around an Elliptic Cylinder—A Numerical Study,” ASME J. Fluids Eng., 135(11), p. 111201. [CrossRef]
Blom, F. J., and Leyland, P., 1998, “Analysis of Fluid–Structure Interaction by Means of Dynamic Unstructured Meshes,” ASME J. Fluids Eng., 120(4), pp. 792–798. [CrossRef]
Lee, E. S., Violeau, D., Laurence, D., Stansby, P., and Moulinec, C., 2007, “SPHERIC Test Case 6: 2-D Incompressible Flow Around a Moving Square Inside a Rectangular Box,” SPHERIC 2nd International Workshop, Madrid, Spain, May 23–25, pp. 37–41.
Capone, T., Panizzo, A., Cecioni, C., and Darlymple, A., 2007, “Accuracy and Stability of Numerical Schemes in SPH,” 2nd SPHERIC International Workshop, A. J. C.Crespo, M.Gomez-Gesteira, A.Souto-Iglesias, L.Delorme, and J. M.Grassa, eds., Madrid, Spain, May 23–25, pp. 156–160.
Morris, J. P., Fox, P. J., and Zhu, Y., 1997, “Modeling Low Reynolds Number Incompressible Flows Using SPH,” J. Comput. Phys., 136(1), pp. 214–226. [CrossRef]
Xu, R., Stansby, P., and Laurence, D., 2009, “Accuracy and Stability in Incompressible SPH (ISPH) Based on the Projection Method and a New Approach,” J. Comput. Phys., 228(18), pp. 6703–6725. [CrossRef]
Ma, J., Ge, W., Wang, X., Wang, J., and Li, J., 2006, “High-Resolution Simulation of Gas–Solid Suspension Using Macro-Scale Particle Methods,” Chem. Eng. Sci., 61(21), pp. 7096–7106. [CrossRef]
Xiong, Q., Li, B., Chen, F., Ma, J., Ge, W., and Li, J., 2010, “Direct Numerical Simulation of Sub-Grid Structures in Gas–Solid Flow-GPU Implementation of Macro-Scale Pseudo-Particle Modeling,” Chem. Eng. Sci., 65(19), pp. 5356–5365. [CrossRef]
Ghia, U., Ghia, K. N., and Shin, C. T., 1982, “High-Resolutions for Incompressible Flow Using the Navier–Stokes Equations and a Multigrid Method,” J. Comput. Phys., 48(3), pp. 387–411. [CrossRef]
Nestor, R., Basa, M., and Quinlan, N., 2008, “Moving Boundary Problems in the Finite Volume Particle Method,” 3rd ERCOFTAC SPHERIC Workshop on SPH Applications, Lausanne, Switzerland, June 4–6, pp. 109–114.
Shadloo, M. S., Zainali, A., Sadek, S. H., and Yildiz, M., 2011, “Improved Incompressible Smoothed Particle Hydrodynamics Method for Simulating Flow Around Bluff Bodies,” Comput. Methods Appl. Mech. Eng., 200(9–12), pp. 1008–1020. [CrossRef]
Ozalp, A. A., and Dincer, I., 2010, “Laminar Boundary Layer Development Around a Circular Cylinder: Fluid Flow and Heat-Mass Transfer Characteristics,” ASME J. Heat. Transfer, 132(12), p. 121703. [CrossRef]
Celik, B., Raisee, M., and Beskok, A., 2010, “Heat Transfer Enhancement in a Slot Channel Via a Transversely Oscillating Adiabatic Circular Cylinder,” Int. J. Heat Mass Transfer, 53(4), pp. 626–634. [CrossRef]


Grahic Jump Location
Fig. 1

The horizontal (above plots) and vertical (bottom plots) velocity profiles, respectively, in vertical and horizontal middle sections of the lid driven cavity for Re = 400 (left) and Re = 1000 (right)

Grahic Jump Location
Fig. 2

The streamlines produced by the present SPH simulation for the cases with 160 × 160 particles for Re = 400 (left), Re = 1000 (right)

Grahic Jump Location
Fig. 3

Initial state (t = 0) of square in the rectangular cavity

Grahic Jump Location
Fig. 9

Velocity profiles in the wake region for the Re = 40 case in comparison with the Ozalp and Dincer [37] data

Grahic Jump Location
Fig. 7

SPH simulation of flow regimes past a stationary confined circular cylinder for Re = 40 and Re = 100

Grahic Jump Location
Fig. 8

Patterns of vorticity contour for stationary confined circular cylinder at Re = 100

Grahic Jump Location
Fig. 4

Contour of the velocity magnitude of the force motion of the square for Re = 150 in the initially stationary flow for simulation of Lee et al. [28] (top) and present SPH algorithm simulation (bottom)

Grahic Jump Location
Fig. 5

Time variations of the pressure drag coefficient for incompressible FDM [28], FVPM [35], standard WCSPH, and present SPH method

Grahic Jump Location
Fig. 6

Schematic of a channel confined flow over a circular cylinder

Grahic Jump Location
Fig. 10

Variation of nondimensional Lift force versus nondimensional time for F = 1.25

Grahic Jump Location
Fig. 11

Vorticity contours for flows with F = 0.75, F = 1.00, and F = 1.25 at Re = 100

Grahic Jump Location
Fig. 12

Streamlines (von Karman streets) behind the oscillating cylinder for F = 0.75, F = 1.00, and F = 1.25 at Re = 100



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In