Truncation error in mesh-free particle methods

International Journal for Numerical Methods in Engineering

Volumn 66, Issue 13, 2006, Pages 2064-2085

  Quinlan, Nathan J ^a   Basa, M ^a   Lastiwka, M ^a  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

Error analysis; Meshfree methods; Meshless methods; Particle methods; Smoothed particle hydrodynamics

Indexed keywords

COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS;

MESH-FREE PARTICLE METHODS; SMOOTHED PARTICLE HYDRODYNAMICS; TRUNCATION ERROR;

NUMERICAL METHODS;

COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; MATHEMATICAL MODELS; NUMERICAL METHODS; PARTICLE SIZE ANALYSIS;

EID: 33745623093     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1617     Document Type: Article

References (30)

1. Lucy LB. A numerical approach to the testing of fission hypothesis. Astronomical Journal 1977; 82:1013-1024.
2. Monaghan JJ, Gingold RA. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 1977; 181:375-389.
3. Monaghan JJ. Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics 1992; 30: 543-574.
4. Monaghan JJ. New developments in smoothed particle hydrodynamics. In Meshfree Methods for Partial Differential Equations, Griebel M, Schweitzer MA (eds), Lecture Notes in Computational Science and Engineering, vol. 26. Springer: Berlin, 2003.
5. Monaghan JJ. Smoothed particle hydrodynamics. Reports on Progress in Physics 2005; 68:1703-1759.
6. Randles PW, Libersky LD. Smoothed particle hydrodynamics: some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):375-408.
7. Vignjevic R. Review of development of the smooth particle hydrodynamics (SPH) method. Sixth Conference on Dynamics and Control of Systems and Structures in Space, Riomaggiore, Italy, July 2004.
8. Li S, Liu WK. Meshfree Particle Methods. Springer: Berlin, 2004.
9. Liu GR, Liu MB. Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific: Singapore 2003.
10. Monaghan JJ. Simulating free surface flows with SPH. Journal of Computational Physics 1994; 110(2): 399-406.
11. Cummins SJ, Rudman M. An SPH projection method. Journal of Computational Physics 1999; 152(2): 584-607.
12. Ellero M, Serrano M, Español P. On a new incompressible formulation for SPH. In Meshless 2005: Proceedings of the ECCOMAS Thematic Conference on Meshless Methods, Leitão VMA, Alves CJS, Duarte CA (eds). DM-IST: Lisbon, 2005.
13. Lastiwka M, Basa M, Quinlan NJ. Incompressible smoothed particle hydrodynamics using a Clebsch-Weber decomposition. In Meshless 2005: Proceedings of the ECCOMAS Thematic Conference on Meshless Methods, Leitão VMA, Alves CJS, Duarte CA (eds). DM-IST: Lisbon, 2005.
14. Takeda H, Miyama SM, Sekiya M. Numerical simulation of viscous flow by smoothed particle hydrodynamics. Progress of Theoretical Physics 1999; 92(5):939-960.
15. Sigalotti LG, Klapp J, Sira E, Mclean Y, Hasmy A. SPH simulations of time-dependent Poiseuille flow at low Reynolds numbers. Journal of Computational Physics 2003; 191(2):622-639.
16. Basa M, Lastiwka M, Quinlan NJ. Poiseuille flow with SPH: effects of viscosity and boundary implementation. In Meshless 2005: Proceedings of the ECCOMAS Thematic Conference on Meshless Methods, Leitão VMA, Alves CJS, Duarte CA (eds). DM-IST: Lisbon, 2005.
17. Violeau D. One- and two-equations turbulent closures for smoothed particle hydrodynamics. In Hydroinformatics: Proceedings of the 6th International Conference, Liong S-Y, Phoon K-K, Babovic V (eds). World Scientific: Singapore, 2004.
18. Issa R. Numerical assessment of the smoothed particle hydrodynamics gridless method for incompressible flows and its extension to turbulent flows. Ph.D. Thesis, University of Manchester, 2005.
19. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106.
20. Dilts GA. Moving-least-squares-particle-hydrodynamics - I. Consistency and stability. International Journal for Numerical Methods in Engineering 1999; 44(8):1115-1155.
21. Bonet J, Lok T-SL. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering 1999; 180(1-2):97-115.
22. Liu MB, Liu GR, Lam KY. Constructing smoothing functions in smoothed particle hydrodynamics with applications. Journal of Computational and Applied Mathematics 2003; 155(2):263-284.
23. Meglicki Z. Verification and accuracy of smoothed particle magnetohydrodynamics. Computer Physics Communications 1993; 81(1-2):91-104.
24. Fulk DA, Quinn DW. An analysis of 1-D smoothed particle hydrodynamics kernels. Journal of Computational Physics 1996; 126(1):165-180.
25. Cleary PW, Monaghan JJ. Conduction modelling using smoothed particle hydrodynamics. Journal of Computational Physics 1999; 148(1):227-264.
26. Han W, Meng X. Error analysis of the reproducing kernel particle method. Computer Methods in Applied Mechanics and Engineering 2001; 190(46-47):6157-6181.
27. Monaghan JJ, Lattanzio JC. A refined particle method for astrophysical problems. Astronomy and Astrophysics 1985; 149(1):135-143.
28. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):3-47.
29. Ralston A. A First Course in Numerical Analysis. McGraw-Hill: New York, 1965.
30. Yakowitz S, Krimmel JE, Szidarovszky F. Weighted Monte Carlo integration. SIAM Journal on Numerical Analysis 1978; 15(6):1289-1300.