On discretization of second-order derivatives in Smoothed Particle Hydrodynamics

World Academy of Science, Engineering and Technology

Volumn 40, Issue , 2009, Pages 243-246

  Fatehi, R ^a   Fayazbakhsh, M A ^a   Manzari, M T ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Heat conduction; Meshfree methods; Second order derivatives; Smoothed Particle Hydrodynamics (SPH)

Indexed keywords

DIFFERENCE SCHEMES; DISCRETIZATIONS; HEAT EQUATION; HIGH-ORDER KERNELS; INFLECTION POINTS; INITIAL CONDITIONS; KERNEL FUNCTION; MESH-FREE METHOD; MESHFREE METHODS; NONLINEAR COEFFICIENT; PARTICLE DISTANCE; PHYSICAL OSCILLATIONS; SECOND ORDERS; SECOND-ORDER DERIVATIVES; SMOOTHED PARTICLE HYDRODYNAMICS; SMOOTHED PARTICLE HYDRODYNAMICS (SPH); SPATIAL DERIVATIVES; STEP FUNCTIONS; TRANSIENT RESPONSE; UNSTEADY HEAT CONDUCTION;

DIFFERENCE EQUATIONS; HEAT CONDUCTION; HYDRODYNAMICS;

FLUID DYNAMICS;

EID: 78651584036     PISSN: 2010376X     EISSN: 20103778     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. L. Lucy, "A numerical approach to the testing of fission hypothesis," Astrophysical Journal, vol. 82, pp. 1013-1020, 1977.
2. R. Gingold and J. Monaghan, "Smoothed particle hydrodynamics: Theory and application to nonspherical stars," Astrophysical Journal, vol. 181, pp. 275-389, 1977.
3. R. Gingold and J. Monaghan, "Kernel estimates as a basis for general particle methods in hydrodynamics," Journal of Computational Physics, vol. 46, pp. 429- 453,1982.
4. J. Monaghan, "Simulating free surface flows with sph," Journal of Computational Physics, vol. 110, pp. 399-406, 1994.
5. H. Takeda, S. Miyama, and M. Sekiya, "Numerical simulation of viscous flow by smoothed particle hydrodynamics," Progress of Theoretical Physics, vol. 92, no. 5, pp. 939-960, 1994.
6. J. Morris, P. Fox, and Y. Zhu, "Modeling low reynolds number incompressible flows using sph," Journal of Computational Physics, vol. 136, no. 1, pp. 214-226, 1997.
7. J. Monaghan, "Smoothed particle hydrodynamics," Reports on Progress in Physics, vol. 68, pp. 1703-1759, 2005.
8. O. Flebbe, S. Munzel, H. Herold, H. Riffert, and H. Ruder, "Smoothed particle hydrodynamics-physical viscosity and the simulation of accre- tion disks," The Astrophysical Journal, vol. 431, pp. 214-226, 1994.
9. S. Watkins, A. Bhattal, N. Francis, T. J.A., and Whitworth, "A new prescription for viscosity in smoothed particle hydrodynamics," Astronomy and Astrophysics, vol. 119, pp. 177-187, 1996.
10. J. Jeong, M. Jhon, J. Halow, and J. van Osdol, "Smoothed particle hydrodynamics: Applications to heat conduction," Computer Physics Communications, vol. 153, no. 1, pp. 71-84, 2003.
11. J. Bonet and T. Lok, "Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations," Computer Methods in Applied Mechanics and Engineering, vol. 180, no. 1-2, pp. 97-115, 1999.
12. S. Nugent and H. Posch, "Liquid drops and surface tension with smoothed particle applied mechanics," Physical Review E, vol. 62, no. 4, pp. 4968-4975, 2000.
13. J. Bonet, S. Kulasegaram, M. Rodriguez-Paz, and M. Profit, "Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems," Computer Methods in Applied Mechanics and Engineering, vol. 193, no. 12-14, pp. 1245-1256, 2004.
14. Y. Meleán, L. Sigalotti, and A. Hasmy, "On the SPH tensile instability in forming viscous liquid drops," Computer Physics Communications, vol. 157, no. 3, pp. 191-200, 2004.
15. H. López and L. Sigalotti, "Oscillation of viscous drops with smoothed particle hydrodynamics," Physical Review E, vol. 73, no. 5, p. 51201, 2006.
16. A. Chaniotis, D. Poulikakos, and P. Kououtsakos, "Remeshed smoothed particle hydrodynamics for the simulations of viscous and heat con- ducting flows," Journal of Computational Physics, vol. 182, pp. 67-90, 2002.
17. P. Cleary, "Modelling confined multi-material heat and mass flows using sph," Applied Mathematical Modelling, vol. 22, pp. 981-993, 1998.
18. J. Monaghan and J. Lattanzio, "A refined particle method for astrophysical problems," Astronomy and Astrophysics, vol. 149, no. 1, pp. 135-143, 1985.
19. I. Schoenberg, "Contributions to the problem of approximation of equidistant data by analytic functions. Part A - On the problem of smoothing or graduation. A first class of analytic approximation formulas," Quarterly of Applied Mathematics, vol. 4, pp. 45-99, 1946.