Robustness and accuracy of SPH formulations for viscous flow

International Journal for Numerical Methods in Fluids

Volumn 60, Issue 10, 2009, Pages 1127-1148

  Basa, Mihai ^a   Quinlan, Nathan J ^a   Lastiwka, Martin ^a  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

Boundary conditions; Instability; Lid driven cavity; Mesh free; Poiseuille; Truncation error

Indexed keywords

INSTABILITY; LID-DRIVEN CAVITY; MESH-FREE; POISEUILLE; TRUNCATION ERROR;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL MECHANICS; FLUID DYNAMICS; REYNOLDS NUMBER; VISCOUS FLOW;

STABILITY;

EID: 70349636692     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1927     Document Type: Article

References (30)

1. Monaghan JJ. Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics 1992; 30: 543-574.
2. Speith R, Riffert H. The viscous gas ring as an astrophysical test problem for a viscous SPH-code. Journal of Computational and Applied Mathematics 1999; 109:231-242.
3. Monaghan JJ, Kocharyan A. SPH simulation of multi-phase flow. Computer Physics Communications 1995; 2: 225-235.
4. Violeau D, Issa R. Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview. International Journal for Numerical Methods in Fluids 2007; 53:277-304.
5. Morris JP, Fox PJ, Zhu Y. Modeling low Reynolds number incompressible flows using SPH. Journal of Computational Physics 1997; 136:214-226.
6. Anderson JD. Computational Fluid Dynamics: The Basics with Applications. McGraw-Hill: New York, 1995, ISBN 0-07-001685-2.
7. Bonet J, Lok T-S. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering 1999; 180:97-115.
8. Batchelor GK. An Introduction to Fluid Dynamics. Cambridge University Press: Cambridge, 1967.
9. Quinlan NJ, Basa M, Lastiwka M. Truncation error in mesh-free particle methods. International Journal for Numerical Methods in Engineering 2006; 66(13):2064-2085.
10. Watkins SJ, Bhattal AS, Francis N, Turner JA, Whitworth AP. A new prescription for viscosity in smooth particle hydrodynamics. Astronomy and Astrophysics Supplement Series 1996; 119(1):177-187.
11. Sigalotti LDG, Klapp J, Sira E, Melean Y, Hasmy A. SPH simulations of time-dependent Poiseuille flow at low Reynolds numbers. Journal of Computational Physics 2003; 191:622-638.
12. Chaniotis AK, Poulikakos D, Koumoutsakos P. Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. Journal of Computational Physics 2002; 182(1):67-90.
13. Monaghan JJ. On the problem of penetration in particle methods. Journal of Computational Physics 1989; 82(1):1-15.
14. Li S, Liu WK. Meshfree Particle Methods. Springer: Berlin, 2004.
15. Shepard D. A two-dimensional interpolation function for irregularly-spaced data. Association for Computing Machinery, Proceedings of the 1968 23rd ACM National Conference, New York, NY, U.S.A., 1968; 517-524.
16. Takeda H, Miyama SM, Sekiya M. Numerical simulation of viscous flow by smoothed particle hydrodynamics. Progress of Theoretical Physics 1994; 92(5):939-960.
17. Flebbe O, Munzel S, Herold H, Riffert H, Ruder H. Smoothed particle hydrodynamics: physical viscosity and the simulation of accretion disks. The Astrophysical Journal 1994; 431:754-760.
18. Monaghan JJ, Gingold RA. Shock simulation by the particle method SPH. Journal of Computational Physics 1983; 52:374-389.
19. Brookshaw L. A method of calculating radiative heat diffusion in particle simulations. Astronomical Society of Australia, Proceedings 1985; 6(2):207-210.
20. Cleary PW. Modelling confined multi-material heat and mass flows using SPH. Applied Mathematical Modelling 1998; 22:981-993.
21. Monaghan JJ. Smoothed particle hydrodynamics. Reports on Progress in Physics 2005; 68:1703-1759.
22. Graham DI, Hughes JP. Accuracy of SPH viscous flow models. International Journal for Numerical Methods in Fluids 2007; 56(8):1261-1269.
23. Monaghan JJ, Lattanzio JC. A refined particle method for astrophysical problems. Astronomy and Astrophysics 1985; 149:135-143.
24. Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA. High strain Lagrangian hydrodynamics. A threedimensional SPH code for dynamic material response. Journal of Computational Physics 1993; 109(1):67-75.
25. Hughes JP, Graham DI. Degradation and instability of incompressible SPH computations of simple viscous flows. In Smoothed Particle Hydrodynamics European Research Interest Community - Second International Workshop, Madrid, Spain, Crespo AJC, Gomez-Gesteira M, Souto-Iglesias A, Delorme L, Grassa JM (eds), 2007.
26. Fortin A, Jardak M, Gervais J, Pierre R. Old and new results on the two-dimensional Poiseuille flow. Journal of Computational Physics 1994; 115(2):455-469.
27. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48:387-411.
28. Chern M, Borthwick A, Taylor RE. Pseudospectral element model for free surface viscous flows. International Journal of Numerical Methods for Heat and Fluid Flow 2005; 15(6):517-554.
29. Rogers B. SPH European research interest community benchmark test 3. http://wiki.manchester.ac.uk/spheric/index.php/Test3 [24 July 2008].
30. OpenFOAM 1.4.1. http://www.openfoam.org.