Improved SPH methods for simulating free surface flows of viscous fluids

Applied Numerical Mathematics

Volumn 59, Issue 2, 2009, Pages 251-271

  Fang, Jiannong ^a   Parriaux, Aurèle ^a   Rentschler, Martin ^a   Ancey, Christophe ^a  

^a EPFL   (Switzerland)

Author keywords

Finite particle method; Free surface flows; Meshless meshfree method; Smoothed Particle Hydrodynamics; Viscous fluids

Indexed keywords

FLUID DYNAMICS; HYDRODYNAMICS; INCOMPRESSIBLE FLOW; POLYNOMIAL APPROXIMATION; VISCOUS FLOW;

FINITE PARTICLE METHOD; FREE SURFACE FLOWS; MESHLESS/MESHFREE METHOD; SMOOTHED PARTICLE HYDRODYNAMICS; VISCOUS FLUIDS;

SURFACES;

EID: 56249122631     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.02.003     Document Type: Article

References (47)

1. Ata R., and Soulaïmani A. A stabilized SPH method for inviscid shallow water flows. Int. J. Numer. Methods Fluids 47 (2005) 139-159
2. Benz W., and Asphaug E. Simulations of brittle solids using smooth particle hydrodynamics. Comput. Phys. Commun. 87 (1995) 253-265
3. Bonet J., and Lok T.-S.L. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput. Methods Appl. Mech. Engrg. 180 (1999) 97-115
4. Børve S., Omang M., and Trulsen J. Regularized smoothed particle hydrodynamics: A new approach to simulating magnetohydrodynamic shocks. Astrophys. J. 561 (2001) 82-93
5. Chaniotis A., Poulikakos D., and Koumoutsakos P. Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. J. Comput. Phys. 182 (2002) 67-90
6. Chen J.K., and Beraun J.E. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Comput. Methods Appl. Mech. Engrg. 190 (2000) 225-239
7. Cleary P.W., and Monaghan J.J. Conduction modeling using smoothed particle hydrodynamics. J. Comput. Phys. 148 (1999) 227-264
8. Cleary P.W., and Prakash M. Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences. Philos. Trans. R. Soc. Lond. A 362 (2004) 2003-2030
9. A. Colagrossi, A meshless Lagrangian method for free-surface and interface flows with fragmentation, Ph.D. thesis, Università di Roma La Sapienza, 2005
10. Cummins S.J., and Rudman M. An SPH projection method. J. Comput. Phys. 152 (1999) 584-607
11. Dilts G.A. Moving least square particle hydrodynamics I: consistency and stability. Int. J. Numer. Methods Engrg. 44 (1999) 1115-1155
12. Dilts G.A. Moving least-squares particle hydrodynamics II: Conservation and boundaries. Int. J. Numer. Methods Engrg. 48 (2000) 1503-1524
13. Ellero M., Kröger M., and Hess S. Viscoelastic flows studied by smoothed particle dynamics. J. Non-Newtonian Fluid Mech. 105 (2002) 35-51
14. Ellero M., and Tanner R.I. SPH simulations of transient viscoelastic flows at low Reynolds number. J. Non-Newtonian Fluid Mech. 132 (2005) 61-72
15. Español P., and Revenga M. Smoothed dissipative particle dynamics. Phys. Rev. E 67 (2003) 267051-2670512
16. Fang J., Owens R.G., Tacher L., and Parriaux A. A numerical study of the SPH method for simulating transient viscoelastic free surface flows. J. Non-Newtonian Fluid Mech. 139 (2006) 68-84
17. Flebbe O., Munzel S., Herold H., Riffert H., and Ruder H. Smoothed particle hydrodynamics - physical viscosity and the simulation of accretion disks. Astrophys. J. 431 (1994) 754-760
18. Gingold R.A., and Monaghan J.J. Smoothed particle hydrodynamics theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181 (1977) 375-389
19. Grmela M., and Öttinger H.C. Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56 (1997) 6620-6632
20. Hockney R.W., and Eastwood J.W. Computer Simulation Using Particles (1981), McGraw-Hill, New York
21. Hoover W.G., Hoover C.G., and Merritt E.C. Smooth particle applied mechanics: conservation of angular momentum with tensile stability and velocity averaging. Phys. Rev. E 69 (2004) 016702-1-10
22. Johnson G.R., and Beissel S.R. Normalised smoothing functions for SPH impact computations. Int. J. Numer. Methods Engrg. 39 (1996) 2725-2741
23. Libersky L.D., and Petschek A.G. Smooth particle hydrodynamics with strength of materials. In: Trease H.E., Fritts M.J., and Crowley W.P. (Eds). Advances in the Free-Lagrange Method. Moran, WY, USA, June 1990. Lecture Notes in Phys. vol. 395 (1991), Springer-Verlag, New York/Berlin 248-257
24. Libersky L.D., Petschek A.G., Carney T.C., Hipp J.R., and Allahdadi F.A. High strain Lagrangian hydrodynamics. J. Comput. Phys. 109 (1993) 67-75
25. Liu G.R., and Liu M.B. Smoothed Particle Hydrodynamics - A Meshfree Particle Method (2003), World Scientific
26. Liu M.B., Xie W.P., and Liu G.R. Modeling incompressible flows using a finite particle method. Appl. Math. Model. 29 (2005) 1252-1270
27. Liu W.K., Jun S., and Zhang Y.F. Reproducing kernel particle methods. Int. J. Numer. Methods Fluids 20 (1995) 1081-1106
28. Lucy L.B. A numerical approach to the testing of the fission hypothesis. Astron. J. 83 (1977) 1013-1024
29. Maveyraud C., Benz W., Sornette A., and Sornette D. Solid friction at high sliding velocities: an explicit three-dimensional dynamical smoothed particle hydrodynamics approach. J. Geophys. Res. 104 (1999) 28769-28788
30. Monaghan J.J. Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30 (1992) 543-574
31. Monaghan J.J. Simulating free surface flows with SPH. J. Comput. Phys. 110 (1994) 399-406
32. Monaghan J.J. SPH without a tensile instability. J. Comput. Phys. 159 (2000) 290-311
33. Monaghan J.J. SPH compressible turbulence. Mon. Not. R. Astron. Soc. 335 (2002) 843-852
34. Monaghan J.J., and Kocharyan A. SPH simulation of multi-phase flow. Comput. Phys. Commun. 87 (1995) 225-235
35. Monaghan J.J. Smoothed particle hydrodynamics. Rep. Prog. Phys. 68 (2005) 1703-1759
36. Morris J.P. Simulating surface tension with smoothed particle hydrodynamics. Int. J. Numer. Methods Fluids 33 (2000) 333-353
37. Morris J.P., Fox P.J., and Zhu Y. Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136 (1997) 214-226
38. Oger L., and Savage S.B. Smoothed particle hydrodynamics for cohesive grains. Comput. Methods Appl. Mech. Engrg. 180 (1999) 169-183
39. Öttinger H.C., and Grmela M. Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys. Rev. E 56 (1997) 6633-6655
40. Owen J.M., Villumsen J.V., Shapiro P.R., and Martel H. Adaptive smoothed particle hydrodynamics: Methodology. II. Astrophys. J. Suppl. Ser. 116 (1998) 155-209
41. Randles P.W., and Libersky L.D. Smoothed particle hydrodynamics: Some recent improvements and applications. Comput. Methods Appl. Mech. Engrg. 139 (1996) 375-408
42. Shao S., and Lo E.Y.M. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Resour. 26 7 (2003) 787-800
43. Shapiro P.R., Martel H., Villumsen J.V., and Owen J.M. Adaptive smoothed particle hydrodynamics, with application to cosmology: Methodology. Astrophys. J. Suppl. Ser. 103 (1996) 269-330
44. Swegle J.W., Hicks D.L., and Attaway S.W. Smoothed particle hydrodynamics stability analysis. J. Comput. Phys. 116 (1995) 123-134
45. Takeda H., Miyama S.M., and Sekiya M. Numerical simulation of viscous flow by smoothed particle hydrodynamics. Prog. Theor. Phys. 92 5 (1994) 939-959
46. Watkins S.J., Bhattal A.S., Francis N., Turner J.A., and Whitworth A.P. A new prescription for viscosity in smoothed particle hydrodynamics. Astron. Astrophys. Suppl. Ser. 119 (1996) 177-187
47. Zhang G.M., and Batra R.C. Modified smoothed particle hydrodynamics method and its applications to transient problems. Comput. Mech. 34 (2004) 137-146